--- _id: '14499' abstract: - lang: eng text: "An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes." acknowledgement: Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research Fellowship. article_number: e21 article_processing_charge: Yes article_type: original author: - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Ashwin full_name: Sah, Ashwin last_name: Sah - first_name: Lisa full_name: Sauermann, Lisa last_name: Sauermann - first_name: Mehtaab full_name: Sawhney, Mehtaab last_name: Sawhney citation: ama: Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 2023;11. doi:10.1017/fmp.2023.17 apa: Kwan, M. A., Sah, A., Sauermann, L., & Sawhney, M. (2023). Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. Cambridge University Press. https://doi.org/10.1017/fmp.2023.17 chicago: Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” Forum of Mathematics, Pi. Cambridge University Press, 2023. https://doi.org/10.1017/fmp.2023.17. ieee: M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture,” Forum of Mathematics, Pi, vol. 11. Cambridge University Press, 2023. ista: Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11, e21. mla: Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” Forum of Mathematics, Pi, vol. 11, e21, Cambridge University Press, 2023, doi:10.1017/fmp.2023.17. short: M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11 (2023). date_created: 2023-11-07T09:02:48Z date_published: 2023-08-24T00:00:00Z date_updated: 2023-11-07T09:18:57Z day: '24' ddc: - '510' department: - _id: MaKw doi: 10.1017/fmp.2023.17 external_id: arxiv: - '2208.02874' file: - access_level: open_access checksum: 54b824098d59073cc87a308d458b0a3e content_type: application/pdf creator: dernst date_created: 2023-11-07T09:16:23Z date_updated: 2023-11-07T09:16:23Z file_id: '14500' file_name: 2023_ForumMathematics_Kwan.pdf file_size: 1218719 relation: main_file success: 1 file_date_updated: 2023-11-07T09:16:23Z has_accepted_license: '1' intvolume: ' 11' keyword: - Discrete Mathematics and Combinatorics - Geometry and Topology - Mathematical Physics - Statistics and Probability - Algebra and Number Theory - Analysis language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: bd95085b-d553-11ed-ba76-e55d3349be45 grant_number: '101076777' name: Randomness and structure in combinatorics publication: Forum of Mathematics, Pi publication_identifier: issn: - 2050-5086 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '14192' abstract: - lang: eng text: For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling. acknowledgement: D.M. and K.M. thank Robert Seiringer for helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria). Financial support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016, ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon 2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.) is gratefully acknowledged. article_number: '17' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Jonas full_name: Lampart, Jonas last_name: Lampart - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Krzysztof full_name: Mysliwy, Krzysztof id: 316457FC-F248-11E8-B48F-1D18A9856A87 last_name: Mysliwy citation: ama: Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 2023;26(3). doi:10.1007/s11040-023-09460-x apa: Lampart, J., Mitrouskas, D. J., & Mysliwy, K. (2023). On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-023-09460-x chicago: Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2023. https://doi.org/10.1007/s11040-023-09460-x. ieee: J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the energy–momentum relation for the polaron,” Mathematical Physics, Analysis and Geometry, vol. 26, no. 3. Springer Nature, 2023. ista: Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3), 17. mla: Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical Physics, Analysis and Geometry, vol. 26, no. 3, 17, Springer Nature, 2023, doi:10.1007/s11040-023-09460-x. short: J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and Geometry 26 (2023). date_created: 2023-08-22T14:09:47Z date_published: 2023-07-26T00:00:00Z date_updated: 2023-12-13T12:16:19Z day: '26' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11040-023-09460-x external_id: arxiv: - '2206.14708' isi: - '001032992600001' file: - access_level: open_access checksum: f0941cc66cb3ed06a12ca4b7e356cfd6 content_type: application/pdf creator: dernst date_created: 2023-08-23T10:59:15Z date_updated: 2023-08-23T10:59:15Z file_id: '14225' file_name: 2023_MathPhysics_Lampart.pdf file_size: 317026 relation: main_file success: 1 file_date_updated: 2023-08-23T10:59:15Z has_accepted_license: '1' intvolume: ' 26' isi: 1 issue: '3' keyword: - Geometry and Topology - Mathematical Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version publication: Mathematical Physics, Analysis and Geometry publication_identifier: eissn: - 1572-9656 issn: - 1385-0172 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the global minimum of the energy–momentum relation for the polaron tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2023' ... --- _id: '14756' abstract: - lang: eng text: "We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r: the 2-groupoid of 2-dimensional fully extended r-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced Spin 2r -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the rth power of their Serre automorphisms. For r=1, we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r=2.\r\nTo construct examples, we explicitly describe Spin 2r​-homotopy fixed points in the equivariant completion of any symmetric monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg models gives rise to fully extended spin TQFTs and that half of these do not factor through the oriented bordism 2-category." acknowledgement: "N.C. is supported by the DFG Heisenberg Programme.\r\nWe are grateful to Tobias Dyckerhoff, Lukas Müller, Ingo Runkel, and Christopher Schommer-Pries for helpful discussions." article_processing_charge: Yes article_type: original author: - first_name: Nils full_name: Carqueville, Nils last_name: Carqueville - first_name: Lorant full_name: Szegedy, Lorant id: 7943226E-220E-11EA-94C7-D59F3DDC885E last_name: Szegedy orcid: 0000-0003-2834-5054 citation: ama: Carqueville N, Szegedy L. Fully extended r-spin TQFTs. Quantum Topology. 2023;14(3):467-532. doi:10.4171/qt/193 apa: Carqueville, N., & Szegedy, L. (2023). Fully extended r-spin TQFTs. Quantum Topology. European Mathematical Society. https://doi.org/10.4171/qt/193 chicago: Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum Topology. European Mathematical Society, 2023. https://doi.org/10.4171/qt/193. ieee: N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” Quantum Topology, vol. 14, no. 3. European Mathematical Society, pp. 467–532, 2023. ista: Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532. mla: Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum Topology, vol. 14, no. 3, European Mathematical Society, 2023, pp. 467–532, doi:10.4171/qt/193. short: N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532. date_created: 2024-01-08T13:14:48Z date_published: 2023-10-16T00:00:00Z date_updated: 2024-01-09T09:27:46Z day: '16' ddc: - '530' department: - _id: MiLe doi: 10.4171/qt/193 file: - access_level: open_access checksum: b0590aff6e7ec89cc149ba94d459d3a3 content_type: application/pdf creator: dernst date_created: 2024-01-09T09:25:34Z date_updated: 2024-01-09T09:25:34Z file_id: '14764' file_name: 2023_QuantumTopol_Carqueville.pdf file_size: 707344 relation: main_file success: 1 file_date_updated: 2024-01-09T09:25:34Z has_accepted_license: '1' intvolume: ' 14' issue: '3' keyword: - Geometry and Topology - Mathematical Physics language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 467-532 publication: Quantum Topology publication_identifier: issn: - 1663-487X publication_status: published publisher: European Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Fully extended r-spin TQFTs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2023' ... --- _id: '10600' abstract: - lang: eng text: We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article. acknowledgement: J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331. article_number: '011901' article_processing_charge: No article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel citation: ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632' apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0051632' chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.' ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” Journal of Mathematical Physics, vol. 63, no. 1. AIP Publishing, 2022.' ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.' mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.' short: S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022). date_created: 2022-01-03T12:19:48Z date_published: 2022-01-03T00:00:00Z date_updated: 2023-08-02T13:44:32Z day: '03' department: - _id: GradSch - _id: LaEr doi: 10.1063/5.0051632 ec_funded: 1 external_id: arxiv: - '2012.15238' isi: - '000739446000009' intvolume: ' 63' isi: 1 issue: '1' keyword: - mathematical physics - statistical and nonlinear physics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2012.15238 month: '01' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' status: public title: 'Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '10642' abstract: - lang: eng text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences. acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL. article_number: '9' article_processing_charge: No article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel - first_name: Tom full_name: Wessel, Tom last_name: Wessel citation: ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y apa: Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y. ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” Letters in Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022. ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9. mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y. short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022). date_created: 2022-01-18T16:18:25Z date_published: 2022-01-18T00:00:00Z date_updated: 2023-08-02T13:57:02Z day: '18' ddc: - '530' department: - _id: GradSch - _id: LaEr doi: 10.1007/s11005-021-01494-y ec_funded: 1 external_id: arxiv: - '2106.13780' isi: - '000744930400001' file: - access_level: open_access checksum: 7e8e69b76e892c305071a4736131fe18 content_type: application/pdf creator: cchlebak date_created: 2022-01-19T09:41:14Z date_updated: 2022-01-19T09:41:14Z file_id: '10647' file_name: 2022_LettersMathPhys_Henheik.pdf file_size: 357547 relation: main_file success: 1 file_date_updated: 2022-01-19T09:41:14Z has_accepted_license: '1' intvolume: ' 112' isi: 1 issue: '1' keyword: - mathematical physics - statistical and nonlinear physics language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Local stability of ground states in locally gapped and weakly interacting quantum spin systems tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 112 year: '2022' ... --- _id: '10643' abstract: - lang: eng text: "We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n" acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged. article_number: e4 article_processing_charge: Yes article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel citation: ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80' apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80' chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.' ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.' ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.' mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.' short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022). date_created: 2022-01-18T16:18:51Z date_published: 2022-01-18T00:00:00Z date_updated: 2023-08-02T13:53:11Z day: '18' ddc: - '510' department: - _id: GradSch - _id: LaEr doi: 10.1017/fms.2021.80 ec_funded: 1 external_id: arxiv: - '2012.15239' isi: - '000743615000001' file: - access_level: open_access checksum: 87592a755adcef22ea590a99dc728dd3 content_type: application/pdf creator: cchlebak date_created: 2022-01-19T09:27:43Z date_updated: 2022-01-19T09:27:43Z file_id: '10646' file_name: 2022_ForumMathSigma_Henheik.pdf file_size: 705323 relation: main_file success: 1 file_date_updated: 2022-01-19T09:27:43Z has_accepted_license: '1' intvolume: ' 10' isi: 1 keyword: - computational mathematics - discrete mathematics and combinatorics - geometry and topology - mathematical physics - statistics and probability - algebra and number theory - theoretical computer science - analysis language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Forum of Mathematics, Sigma publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' status: public title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 10 year: '2022' ... --- _id: '10623' abstract: - lang: eng text: We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory. acknowledgement: I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions. article_number: '3' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: Henheik SJ. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0 apa: Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0 chicago: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0. ieee: S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022. ista: Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3. mla: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0. short: S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022). date_created: 2022-01-13T15:40:53Z date_published: 2022-01-11T00:00:00Z date_updated: 2023-08-02T13:51:52Z day: '11' ddc: - '514' department: - _id: GradSch - _id: LaEr doi: 10.1007/s11040-021-09415-0 ec_funded: 1 external_id: arxiv: - '2106.02015' isi: - '000741387600001' file: - access_level: open_access checksum: d44f8123a52592a75b2c3b8ee2cd2435 content_type: application/pdf creator: cchlebak date_created: 2022-01-14T07:27:45Z date_updated: 2022-01-14T07:27:45Z file_id: '10624' file_name: 2022_MathPhyAnalGeo_Henheik.pdf file_size: 505804 relation: main_file success: 1 file_date_updated: 2022-01-14T07:27:45Z has_accepted_license: '1' intvolume: ' 25' isi: 1 issue: '1' keyword: - geometry and topology - mathematical physics language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Mathematical Physics, Analysis and Geometry publication_identifier: eissn: - 1572-9656 issn: - 1385-0172 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS critical temperature at high density tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 25 year: '2022' ... --- _id: '11783' abstract: - lang: eng text: We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix. acknowledgement: "The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged." article_number: '061102' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lea full_name: Bossmann, Lea id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425 last_name: Bossmann orcid: 0000-0002-6854-1343 citation: ama: Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 2022;63(6). doi:10.1063/5.0089983 apa: Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0089983 chicago: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0089983. ieee: L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose gas,” Journal of Mathematical Physics, vol. 63, no. 6. AIP Publishing, 2022. ista: Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102. mla: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics, vol. 63, no. 6, 061102, AIP Publishing, 2022, doi:10.1063/5.0089983. short: L. Bossmann, Journal of Mathematical Physics 63 (2022). date_created: 2022-08-11T06:37:52Z date_published: 2022-06-10T00:00:00Z date_updated: 2023-08-03T12:46:28Z day: '10' ddc: - '530' department: - _id: RoSe doi: 10.1063/5.0089983 ec_funded: 1 external_id: arxiv: - '2203.00730' isi: - '000809648100002' file: - access_level: open_access checksum: d0d32c338c1896680174be88c70968fa content_type: application/pdf creator: dernst date_created: 2022-08-11T07:03:02Z date_updated: 2022-08-11T07:03:02Z file_id: '11784' file_name: 2022_JourMathPhysics_Bossmann.pdf file_size: 5957888 relation: main_file success: 1 file_date_updated: 2022-08-11T07:03:02Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '6' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Low-energy spectrum and dynamics of the weakly interacting Bose gas tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '11917' abstract: - lang: eng text: We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to more general interactions. Furthermore, we derive a new lower bound which agrees with the upper bound in leading order. acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding provided by IST Austria." article_number: '9' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4 apa: Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02940-4 chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4. ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly interacting bosons,” Journal of Statistical Physics, vol. 188. Springer Nature, 2022. ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 188, 9. mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188, 9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4. short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022). date_created: 2022-08-18T07:23:26Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-08-03T12:55:58Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s10955-022-02940-4 ec_funded: 1 external_id: isi: - '000805175000001' file: - access_level: open_access checksum: 44418cb44f07fa21ed3907f85abf7f39 content_type: application/pdf creator: dernst date_created: 2022-08-18T08:09:00Z date_updated: 2022-08-18T08:09:00Z file_id: '11922' file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf file_size: 483481 relation: main_file success: 1 file_date_updated: 2022-08-18T08:09:00Z has_accepted_license: '1' intvolume: ' 188' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Large deviation estimates for weakly interacting bosons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 188 year: '2022' ... --- _id: '12145' abstract: - lang: eng text: In the class of strictly convex smooth boundaries each of which has no strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugate near their respective boundaries, and C∞-conjugate, near the boundary and away from a line passing through the center of the underlying ellipse. We also prove that, if the billiard maps corresponding to two ellipses are topologically conjugate, then the two ellipses are similar. acknowledgement: "We are grateful to the anonymous referees for their careful reading and valuable remarks and\r\ncomments which helped to improve the paper significantly. We gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885707)." article_processing_charge: No article_type: original author: - first_name: Edmond full_name: Koudjinan, Edmond id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E last_name: Koudjinan orcid: 0000-0003-2640-4049 - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 2022;27(6):525-537. doi:10.1134/S1560354722050021 apa: Koudjinan, E., & Kaloshin, V. (2022). On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/S1560354722050021 chicago: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” Regular and Chaotic Dynamics. Springer Nature, 2022. https://doi.org/10.1134/S1560354722050021. ieee: E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under conjugacy,” Regular and Chaotic Dynamics, vol. 27, no. 6. Springer Nature, pp. 525–537, 2022. ista: Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537. mla: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” Regular and Chaotic Dynamics, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:10.1134/S1560354722050021. short: E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537. date_created: 2023-01-12T12:06:49Z date_published: 2022-10-03T00:00:00Z date_updated: 2023-08-04T08:59:14Z day: '03' department: - _id: VaKa doi: 10.1134/S1560354722050021 ec_funded: 1 external_id: arxiv: - '2105.14640' isi: - '000865267300002' intvolume: ' 27' isi: 1 issue: '6' keyword: - Mechanical Engineering - Applied Mathematics - Mathematical Physics - Modeling and Simulation - Statistical and Nonlinear Physics - Mathematics (miscellaneous) language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.14640 month: '10' oa: 1 oa_version: Preprint page: 525-537 project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Regular and Chaotic Dynamics publication_identifier: eissn: - 1468-4845 issn: - 1560-3547 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1134/s1560354722060107 scopus_import: '1' status: public title: On some invariants of Birkhoff billiards under conjugacy type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 27 year: '2022' ... --- _id: '12148' abstract: - lang: eng text: 'We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.' acknowledgement: L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. article_number: e96 article_processing_charge: No article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96. mla: Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86. short: G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022). date_created: 2023-01-12T12:07:30Z date_published: 2022-10-27T00:00:00Z date_updated: 2023-08-04T09:00:35Z day: '27' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2022.86 ec_funded: 1 external_id: isi: - '000873719200001' file: - access_level: open_access checksum: 94a049aeb1eea5497aa097712a73c400 content_type: application/pdf creator: dernst date_created: 2023-01-24T10:02:40Z date_updated: 2023-01-24T10:02:40Z file_id: '12356' file_name: 2022_ForumMath_Cipolloni.pdf file_size: 817089 relation: main_file success: 1 file_date_updated: 2023-01-24T10:02:40Z has_accepted_license: '1' intvolume: ' 10' isi: 1 keyword: - Computational Mathematics - Discrete Mathematics and Combinatorics - Geometry and Topology - Mathematical Physics - Statistics and Probability - Algebra and Number Theory - Theoretical Computer Science - Analysis language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Rank-uniform local law for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 10 year: '2022' ... --- _id: '12232' abstract: - lang: eng text: We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold. acknowledgement: Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. article_processing_charge: No article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002. doi:10.1007/s00023-022-01188-8 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-022-01188-8 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002. mla: Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8. short: G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002. date_created: 2023-01-16T09:50:26Z date_published: 2022-11-01T00:00:00Z date_updated: 2023-08-04T09:33:52Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00023-022-01188-8 external_id: isi: - '000796323500001' file: - access_level: open_access checksum: 5582f059feeb2f63e2eb68197a34d7dc content_type: application/pdf creator: dernst date_created: 2023-01-27T11:06:47Z date_updated: 2023-01-27T11:06:47Z file_id: '12424' file_name: 2022_AnnalesHenriP_Cipolloni.pdf file_size: 1333638 relation: main_file success: 1 file_date_updated: 2023-01-27T11:06:47Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '11' keyword: - Mathematical Physics - Nuclear and High Energy Physics - Statistical and Nonlinear Physics language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 3981-4002 publication: Annales Henri Poincaré publication_identifier: eissn: - 1424-0661 issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Density of small singular values of the shifted real Ginibre ensemble tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 23 year: '2022' ... --- _id: '12243' abstract: - lang: eng text: 'We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ' acknowledgement: "The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation." article_number: '103303' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu citation: ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290 apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104290 chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290. ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022. ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303. mla: Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:10.1063/5.0104290. short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022). date_created: 2023-01-16T09:52:58Z date_published: 2022-10-14T00:00:00Z date_updated: 2023-08-04T09:40:02Z day: '14' ddc: - '510' - '530' department: - _id: LaEr doi: 10.1063/5.0104290 ec_funded: 1 external_id: arxiv: - '2206.04443' isi: - '000869715800001' file: - access_level: open_access checksum: 2db278ae5b07f345a7e3fec1f92b5c33 content_type: application/pdf creator: dernst date_created: 2023-01-30T08:01:10Z date_updated: 2023-01-30T08:01:10Z file_id: '12436' file_name: 2022_JourMathPhysics_Cipolloni2.pdf file_size: 7356807 relation: main_file success: 1 file_date_updated: 2023-01-30T08:01:10Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '10' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Directional extremal statistics for Ginibre eigenvalues tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '12259' abstract: - lang: eng text: 'Theoretical foundations of chaos have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena, e.g., weather, arise in systems with many (formally infinite) degrees of freedom, which limits direct quantitative analysis of such systems using chaos theory. In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer a bridge between low- and high-dimensional chaotic phenomena by allowing for a systematic study of how the former connects to the latter. Specifically, we present experimental results, which show the formation of low-dimensional chaotic attractors upon destabilization of regular dynamics and a final transition to high-dimensional chaos via the merging of distinct chaotic regions through a crisis bifurcation. Moreover, we show that the post-crisis dynamics of the system can be rationalized as consecutive scatterings from the nonattracting chaotic sets with lifetimes following exponential distributions. ' acknowledgement: 'This work was partially funded by the Institute of Science and Technology Austria Interdisciplinary Project Committee Grant “Pilot-Wave Hydrodynamics: Chaos and Quantum Analogies.”' article_number: '093138' article_processing_charge: No article_type: original author: - first_name: George H full_name: Choueiri, George H id: 448BD5BC-F248-11E8-B48F-1D18A9856A87 last_name: Choueiri - first_name: Balachandra full_name: Suri, Balachandra id: 47A5E706-F248-11E8-B48F-1D18A9856A87 last_name: Suri - first_name: Jack full_name: Merrin, Jack id: 4515C308-F248-11E8-B48F-1D18A9856A87 last_name: Merrin orcid: 0000-0001-5145-4609 - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 - first_name: Björn full_name: Hof, Björn id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 - first_name: Nazmi B full_name: Budanur, Nazmi B id: 3EA1010E-F248-11E8-B48F-1D18A9856A87 last_name: Budanur orcid: 0000-0003-0423-5010 citation: ama: 'Choueiri GH, Suri B, Merrin J, Serbyn M, Hof B, Budanur NB. Crises and chaotic scattering in hydrodynamic pilot-wave experiments. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(9). doi:10.1063/5.0102904' apa: 'Choueiri, G. H., Suri, B., Merrin, J., Serbyn, M., Hof, B., & Budanur, N. B. (2022). Crises and chaotic scattering in hydrodynamic pilot-wave experiments. Chaos: An Interdisciplinary Journal of Nonlinear Science. AIP Publishing. https://doi.org/10.1063/5.0102904' chicago: 'Choueiri, George H, Balachandra Suri, Jack Merrin, Maksym Serbyn, Björn Hof, and Nazmi B Budanur. “Crises and Chaotic Scattering in Hydrodynamic Pilot-Wave Experiments.” Chaos: An Interdisciplinary Journal of Nonlinear Science. AIP Publishing, 2022. https://doi.org/10.1063/5.0102904.' ieee: 'G. H. Choueiri, B. Suri, J. Merrin, M. Serbyn, B. Hof, and N. B. Budanur, “Crises and chaotic scattering in hydrodynamic pilot-wave experiments,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32, no. 9. AIP Publishing, 2022.' ista: 'Choueiri GH, Suri B, Merrin J, Serbyn M, Hof B, Budanur NB. 2022. Crises and chaotic scattering in hydrodynamic pilot-wave experiments. Chaos: An Interdisciplinary Journal of Nonlinear Science. 32(9), 093138.' mla: 'Choueiri, George H., et al. “Crises and Chaotic Scattering in Hydrodynamic Pilot-Wave Experiments.” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32, no. 9, 093138, AIP Publishing, 2022, doi:10.1063/5.0102904.' short: 'G.H. Choueiri, B. Suri, J. Merrin, M. Serbyn, B. Hof, N.B. Budanur, Chaos: An Interdisciplinary Journal of Nonlinear Science 32 (2022).' date_created: 2023-01-16T09:58:16Z date_published: 2022-09-26T00:00:00Z date_updated: 2023-08-04T09:51:17Z day: '26' ddc: - '530' department: - _id: MaSe - _id: BjHo - _id: NanoFab doi: 10.1063/5.0102904 external_id: arxiv: - '2206.01531' isi: - '000861009600005' file: - access_level: open_access checksum: 17881eff8b21969359a2dd64620120ba content_type: application/pdf creator: dernst date_created: 2023-01-30T09:41:12Z date_updated: 2023-01-30T09:41:12Z file_id: '12445' file_name: 2022_Chaos_Choueiri.pdf file_size: 3209644 relation: main_file success: 1 file_date_updated: 2023-01-30T09:41:12Z has_accepted_license: '1' intvolume: ' 32' isi: 1 issue: '9' keyword: - Applied Mathematics - General Physics and Astronomy - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '09' oa: 1 oa_version: Published Version publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science' publication_identifier: eissn: - 1089-7682 issn: - 1054-1500 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Crises and chaotic scattering in hydrodynamic pilot-wave experiments tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 32 year: '2022' ... --- _id: '11732' abstract: - lang: eng text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)" article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9 apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9 chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9. ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022. ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5. mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9. short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022). date_created: 2022-08-05T11:36:56Z date_published: 2022-07-29T00:00:00Z date_updated: 2023-09-05T14:57:49Z day: '29' ddc: - '530' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1007/s10955-022-02965-9 ec_funded: 1 external_id: isi: - '000833007200002' file: - access_level: open_access checksum: b398c4dbf65f71d417981d6e366427e9 content_type: application/pdf creator: dernst date_created: 2022-08-08T07:36:34Z date_updated: 2022-08-08T07:36:34Z file_id: '11746' file_name: 2022_JourStatisticalPhysics_Henheik.pdf file_size: 419563 relation: main_file success: 1 file_date_updated: 2022-08-08T07:36:34Z has_accepted_license: '1' intvolume: ' 189' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS energy gap at high density tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 189 year: '2022' ... --- _id: '12246' abstract: - lang: eng text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy. acknowledgement: We would like to thank David Gontier for useful advice on the numerical simulations. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful for the hospitality of the Institut Henri Poincaré in Paris, where part of this work was done. article_number: '92' article_processing_charge: No article_type: original author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Elliott H. full_name: Lieb, Elliott H. last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5 apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-022-01584-5 chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5. ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the indirect and exchange energies,” Letters in Mathematical Physics, vol. 112, no. 5. Springer Nature, 2022. ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92. mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer Nature, 2022, doi:10.1007/s11005-022-01584-5. short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022). date_created: 2023-01-16T09:53:54Z date_published: 2022-09-15T00:00:00Z date_updated: 2023-09-05T15:17:34Z day: '15' department: - _id: RoSe doi: 10.1007/s11005-022-01584-5 ec_funded: 1 external_id: arxiv: - '2203.12473' isi: - '000854762600001' intvolume: ' 112' isi: 1 issue: '5' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2203.12473 month: '09' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Improved Lieb–Oxford bound on the indirect and exchange energies type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 112 year: '2022' ... --- _id: '9285' abstract: - lang: eng text: We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit. article_number: '2060004' article_processing_charge: No article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel citation: ama: 'Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 2021;33(01). doi:10.1142/s0129055x20600041' apa: 'Henheik, S. J., & Teufel, S. (2021). Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600041' chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” Reviews in Mathematical Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600041.' ieee: 'S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results,” Reviews in Mathematical Physics, vol. 33, no. 01. World Scientific Publishing, 2021.' ista: 'Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 33(01), 2060004.' mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” Reviews in Mathematical Physics, vol. 33, no. 01, 2060004, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600041.' short: S.J. Henheik, S. Teufel, Reviews in Mathematical Physics 33 (2021). date_created: 2021-03-26T11:29:46Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-02-23T13:53:59Z day: '01' ddc: - '500' doi: 10.1142/s0129055x20600041 extern: '1' external_id: arxiv: - '2002.08669' has_accepted_license: '1' intvolume: ' 33' issue: '01' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2002.08669 month: '02' oa: 1 oa_version: Preprint publication: Reviews in Mathematical Physics publication_identifier: issn: - 0129-055X - 1793-6659 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: 'Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2021' ... --- _id: '9891' abstract: - lang: eng text: 'Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron gas) with density equal to a characteristic function. This allows us to show that three definitions of the jellium energy coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache [“Equality of the Jellium and uniform electron gas next-order asymptotic terms for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized energy” studied in a series of papers by Serfaty and others, and thus, by the work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2-sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations.' acknowledgement: The author would like to thank Robert Seiringer for guidance and many helpful comments on this project. The author would also like to thank Mathieu Lewin for his comments on the manuscript and Lorenzo Portinale for providing his lecture notes for the course “Mathematics of quantum many-body systems” in spring 2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these lecture notes. article_number: '083305' article_processing_charge: No article_type: original author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 2021;62(8). doi:10.1063/5.0053494 apa: Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0053494 chicago: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics. AIP Publishing, 2021. https://doi.org/10.1063/5.0053494. ieee: A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” Journal of Mathematical Physics, vol. 62, no. 8. AIP Publishing, 2021. ista: Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305. mla: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:10.1063/5.0053494. short: A.B. Lauritsen, Journal of Mathematical Physics 62 (2021). date_created: 2021-08-12T07:08:36Z date_published: 2021-08-01T00:00:00Z date_updated: 2023-08-11T10:29:48Z day: '01' ddc: - '530' department: - _id: GradSch - _id: RoSe doi: 10.1063/5.0053494 external_id: arxiv: - '2103.07975' isi: - '000683960800003' file: - access_level: open_access checksum: d035be2b894c4d50d90ac5ce252e27cd content_type: application/pdf creator: cziletti date_created: 2021-10-27T12:57:06Z date_updated: 2021-10-27T12:57:06Z file_id: '10188' file_name: 2021_JMathPhy_Lauritsen.pdf file_size: 4352640 relation: main_file success: 1 file_date_updated: 2021-10-27T12:57:06Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '8' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '08' oa: 1 oa_version: Published Version publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Floating Wigner crystal and periodic jellium configurations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 62 year: '2021' ... --- _id: '9973' abstract: - lang: eng text: In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors. acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4 apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4 chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04199-4. ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” Communications in Mathematical Physics, vol. 387. Springer Nature, pp. 761–791, 2021. ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791. mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4. short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791. date_created: 2021-08-30T10:07:44Z date_published: 2021-08-30T00:00:00Z date_updated: 2023-08-11T11:09:07Z day: '30' ddc: - '621' department: - _id: JaMa doi: 10.1007/s00220-021-04199-4 ec_funded: 1 external_id: arxiv: - '2007.13506' isi: - '000691214200001' file: - access_level: open_access checksum: 8a602f916b1c2b0dc1159708b7cb204b content_type: application/pdf creator: cchlebak date_created: 2021-09-08T07:34:24Z date_updated: 2021-09-08T09:46:34Z file_id: '9990' file_name: 2021_CommunMathPhys_Wirth.pdf file_size: 505971 relation: main_file file_date_updated: 2021-09-08T09:46:34Z has_accepted_license: '1' intvolume: ' 387' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 761–791 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Complete gradient estimates of quantum Markov semigroups tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 387 year: '2021' ... --- _id: '9121' abstract: - lang: eng text: "We show that the energy gap for the BCS gap equation is\r\nΞ=μ(8e−2+o(1))exp(π2μ−−√a)\r\nin the low density limit μ→0. Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states." acknowledgement: "Most of this work was done as part of the author’s master’s thesis. The author would like to thank Jan Philip Solovej for his supervision of this process.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria)" article_number: '20' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Lauritsen AB. The BCS energy gap at low density. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01358-5 apa: Lauritsen, A. B. (2021). The BCS energy gap at low density. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01358-5 chicago: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01358-5. ieee: A. B. Lauritsen, “The BCS energy gap at low density,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021. ista: Lauritsen AB. 2021. The BCS energy gap at low density. Letters in Mathematical Physics. 111, 20. mla: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” Letters in Mathematical Physics, vol. 111, 20, Springer Nature, 2021, doi:10.1007/s11005-021-01358-5. short: A.B. Lauritsen, Letters in Mathematical Physics 111 (2021). date_created: 2021-02-15T09:27:14Z date_published: 2021-02-12T00:00:00Z date_updated: 2023-09-05T15:17:16Z day: '12' ddc: - '510' department: - _id: GradSch doi: 10.1007/s11005-021-01358-5 external_id: isi: - '000617531900001' file: - access_level: open_access checksum: eaf1b3ff5026f120f0929a5c417dc842 content_type: application/pdf creator: dernst date_created: 2021-02-15T09:31:07Z date_updated: 2021-02-15T09:31:07Z file_id: '9122' file_name: 2021_LettersMathPhysics_Lauritsen.pdf file_size: 329332 relation: main_file success: 1 file_date_updated: 2021-02-15T09:31:07Z has_accepted_license: '1' intvolume: ' 111' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '02' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: The BCS energy gap at low density tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 111 year: '2021' ... --- _id: '10852' abstract: - lang: eng text: ' We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.' acknowledgement: This work was supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo. 694227). article_number: '2060012' article_processing_charge: No article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics. 2021;33(01). doi:10.1142/s0129055x20600120 apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120 chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120. ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical Physics, vol. 33, no. 01. World Scientific Publishing, 2021. ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012. mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120. short: R. Seiringer, Reviews in Mathematical Physics 33 (2021). date_created: 2022-03-18T08:11:34Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-09-05T16:08:02Z day: '01' department: - _id: RoSe doi: 10.1142/s0129055x20600120 ec_funded: 1 external_id: arxiv: - '1912.12509' isi: - '000613313200013' intvolume: ' 33' isi: 1 issue: '01' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1912.12509 month: '02' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: The polaron at strong coupling type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 33 year: '2021' ... --- _id: '8415' abstract: - lang: eng text: 'We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift on three symbols that provides a natural labeling of all periodic orbits. We study the following inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of periodic orbits together with their labeling), determine the geometry of the billiard table? We show that from the Marked Length Spectrum it is possible to recover the curvature at periodic points of period two, as well as the Lyapunov exponent of each periodic orbit.' article_processing_charge: No article_type: original author: - first_name: Péter full_name: Bálint, Péter last_name: Bálint - first_name: Jacopo full_name: De Simoi, Jacopo last_name: De Simoi - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Martin full_name: Leguil, Martin last_name: Leguil citation: ama: Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 2019;374(3):1531-1575. doi:10.1007/s00220-019-03448-x apa: Bálint, P., De Simoi, J., Kaloshin, V., & Leguil, M. (2019). Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03448-x chicago: Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” Communications in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03448-x. ieee: P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards,” Communications in Mathematical Physics, vol. 374, no. 3. Springer Nature, pp. 1531–1575, 2019. ista: Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 374(3), 1531–1575. mla: Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” Communications in Mathematical Physics, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x. short: P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575. date_created: 2020-09-17T10:41:27Z date_published: 2019-05-09T00:00:00Z date_updated: 2021-01-12T08:19:08Z day: '09' doi: 10.1007/s00220-019-03448-x extern: '1' external_id: arxiv: - '1809.08947' intvolume: ' 374' issue: '3' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1809.08947 month: '05' oa: 1 oa_version: Preprint page: 1531-1575 publication: Communications in Mathematical Physics publication_identifier: issn: - 0010-3616 - 1432-0916 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 374 year: '2019' ... --- _id: '8417' abstract: - lang: eng text: The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show the existence of orbits whose angular momentum performs arbitrary excursions in a large region. In particular, there exist diffusive orbits, that is, with a large variation of angular momentum. The leading idea of the proof consists in analyzing parabolic motions of the comet. By a well-known result of McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold at parabolic infinity. On P∞ it is possible to define two scattering maps, which contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic both in the future and the past. Since the inner dynamics inside P∞ is trivial, two different scattering maps are used. The combination of these two scattering maps permits the design of the desired diffusive pseudo-orbits. Using shadowing techniques and these pseudo orbits we show the existence of true trajectories of the RPETBP whose angular momentum varies in any predetermined fashion. article_processing_charge: No article_type: original author: - first_name: Amadeu full_name: Delshams, Amadeu last_name: Delshams - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Abraham full_name: de la Rosa, Abraham last_name: de la Rosa - first_name: Tere M. full_name: Seara, Tere M. last_name: Seara citation: ama: Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 2018;366(3):1173-1228. doi:10.1007/s00220-018-3248-z apa: Delshams, A., Kaloshin, V., de la Rosa, A., & Seara, T. M. (2018). Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-018-3248-z chicago: Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” Communications in Mathematical Physics. Springer Nature, 2018. https://doi.org/10.1007/s00220-018-3248-z. ieee: A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability in the restricted planar elliptic three body problem,” Communications in Mathematical Physics, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018. ista: Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 366(3), 1173–1228. mla: Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” Communications in Mathematical Physics, vol. 366, no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z. short: A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical Physics 366 (2018) 1173–1228. date_created: 2020-09-17T10:41:43Z date_published: 2018-09-05T00:00:00Z date_updated: 2021-01-12T08:19:08Z day: '05' doi: 10.1007/s00220-018-3248-z extern: '1' intvolume: ' 366' issue: '3' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '09' oa_version: None page: 1173-1228 publication: Communications in Mathematical Physics publication_identifier: issn: - 0010-3616 - 1432-0916 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Global instability in the restricted planar elliptic three body problem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 366 year: '2018' ... --- _id: '8420' abstract: - lang: eng text: We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number 1/q is polynomially sense in the smooth case, and exponentially dense in the analytic case. article_processing_charge: No article_type: original author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Ke full_name: Zhang, Ke last_name: Zhang citation: ama: Kaloshin V, Zhang K. Density of convex billiards with rational caustics. Nonlinearity. 2018;31(11):5214-5234. doi:10.1088/1361-6544/aadc12 apa: Kaloshin, V., & Zhang, K. (2018). Density of convex billiards with rational caustics. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/aadc12 chicago: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” Nonlinearity. IOP Publishing, 2018. https://doi.org/10.1088/1361-6544/aadc12. ieee: V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,” Nonlinearity, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018. ista: Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234. mla: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” Nonlinearity, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12. short: V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234. date_created: 2020-09-17T10:42:09Z date_published: 2018-10-15T00:00:00Z date_updated: 2021-01-12T08:19:10Z day: '15' doi: 10.1088/1361-6544/aadc12 extern: '1' external_id: arxiv: - '1706.07968' intvolume: ' 31' issue: '11' keyword: - Mathematical Physics - General Physics and Astronomy - Applied Mathematics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1706.07968 month: '10' oa: 1 oa_version: Preprint page: 5214-5234 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing quality_controlled: '1' status: public title: Density of convex billiards with rational caustics type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2018' ... --- _id: '8498' abstract: - lang: eng text: "In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$ be a 2-dimensional torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ > 0. Our main result says that for a 'generic' time-periodic perturbation of an integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad \\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a 'connected' net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7]." article_processing_charge: No article_type: original author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: K full_name: Zhang, K last_name: Zhang citation: ama: Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. 2015;28(8):2699-2720. doi:10.1088/0951-7715/28/8/2699 apa: Kaloshin, V., & Zhang, K. (2015). Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/28/8/2699 chicago: Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” Nonlinearity. IOP Publishing, 2015. https://doi.org/10.1088/0951-7715/28/8/2699. ieee: V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two and a half degrees of freedom,” Nonlinearity, vol. 28, no. 8. IOP Publishing, pp. 2699–2720, 2015. ista: Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720. mla: Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” Nonlinearity, vol. 28, no. 8, IOP Publishing, 2015, pp. 2699–720, doi:10.1088/0951-7715/28/8/2699. short: V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720. date_created: 2020-09-18T10:46:43Z date_published: 2015-06-30T00:00:00Z date_updated: 2021-01-12T08:19:41Z day: '30' doi: 10.1088/0951-7715/28/8/2699 extern: '1' intvolume: ' 28' issue: '8' keyword: - Mathematical Physics - General Physics and Astronomy - Applied Mathematics - Statistical and Nonlinear Physics language: - iso: eng month: '06' oa_version: None page: 2699-2720 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing quality_controlled: '1' status: public title: Arnold diffusion for smooth convex systems of two and a half degrees of freedom type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2015' ... --- _id: '8502' abstract: - lang: eng text: 'The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface.' article_processing_charge: No article_type: original author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Maria full_name: Saprykina, Maria last_name: Saprykina citation: ama: Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 2012;315(3):643-697. doi:10.1007/s00220-012-1532-x apa: Kaloshin, V., & Saprykina, M. (2012). An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-012-1532-x chicago: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” Communications in Mathematical Physics. Springer Nature, 2012. https://doi.org/10.1007/s00220-012-1532-x. ieee: V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension,” Communications in Mathematical Physics, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012. ista: Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 315(3), 643–697. mla: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” Communications in Mathematical Physics, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97, doi:10.1007/s00220-012-1532-x. short: V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697. date_created: 2020-09-18T10:47:16Z date_published: 2012-11-01T00:00:00Z date_updated: 2021-01-12T08:19:44Z day: '01' doi: 10.1007/s00220-012-1532-x extern: '1' intvolume: ' 315' issue: '3' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '11' oa_version: None page: 643-697 publication: Communications in Mathematical Physics publication_identifier: issn: - 0010-3616 - 1432-0916 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 315 year: '2012' ... --- _id: '8525' abstract: - lang: eng text: Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented. article_processing_charge: No article_type: original author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 2000;211:253-271. doi:10.1007/s002200050811 apa: Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s002200050811 chicago: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” Communications in Mathematical Physics. Springer Nature, 2000. https://doi.org/10.1007/s002200050811. ieee: V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” Communications in Mathematical Physics, vol. 211. Springer Nature, pp. 253–271, 2000. ista: Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271. mla: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” Communications in Mathematical Physics, vol. 211, Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811. short: V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271. date_created: 2020-09-18T10:50:20Z date_published: 2000-04-01T00:00:00Z date_updated: 2021-01-12T08:19:52Z day: '01' doi: 10.1007/s002200050811 extern: '1' intvolume: ' 211' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '04' oa_version: None page: 253-271 publication: Communications in Mathematical Physics publication_identifier: issn: - 0010-3616 - 1432-0916 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Generic diffeomorphisms with superexponential growth of number of periodic orbits type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 211 year: '2000' ... --- _id: '8527' abstract: - lang: eng text: We introduce a new potential-theoretic definition of the dimension spectrum of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if and is a Borel probability measure with compact support in , then under almost every linear transformation from to , the q-dimension of the image of is ; in particular, the q-dimension of is preserved provided . We also present results on the preservation of information dimension and pointwise dimension. Finally, for and q > 2 we give examples for which is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions. article_processing_charge: No article_type: original author: - first_name: Brian R full_name: Hunt, Brian R last_name: Hunt - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 1997;10(5):1031-1046. doi:10.1088/0951-7715/10/5/002 apa: Hunt, B. R., & Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/10/5/002 chicago: Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” Nonlinearity. IOP Publishing, 1997. https://doi.org/10.1088/0951-7715/10/5/002. ieee: B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” Nonlinearity, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997. ista: Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046. mla: Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” Nonlinearity, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:10.1088/0951-7715/10/5/002. short: B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046. date_created: 2020-09-18T10:50:41Z date_published: 1997-06-19T00:00:00Z date_updated: 2021-01-12T08:19:53Z day: '19' doi: 10.1088/0951-7715/10/5/002 extern: '1' intvolume: ' 10' issue: '5' keyword: - Mathematical Physics - General Physics and Astronomy - Applied Mathematics - Statistical and Nonlinear Physics language: - iso: eng month: '06' oa_version: None page: 1031-1046 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing quality_controlled: '1' status: public title: How projections affect the dimension spectrum of fractal measures type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 10 year: '1997' ...