--- OA_place: publisher OA_type: hybrid _id: '14542' abstract: - lang: eng text: "It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit." acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427. article_number: '2360005 ' article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 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 - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 citation: ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2024;36(9). doi:10.1142/s0129055x2360005x apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2024). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2024. https://doi.org/10.1142/s0129055x2360005x. ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics, vol. 36, no. 9. World Scientific Publishing, 2024. ista: Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005. mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:10.1142/s0129055x2360005x. short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024). corr_author: '1' date_created: 2023-11-15T23:48:14Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-04-07T13:01:40Z day: '01' ddc: - '510' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1142/s0129055x2360005x ec_funded: 1 external_id: arxiv: - '2301.05621' isi: - '001099640300002' file: - access_level: open_access checksum: 2b053a4223b4db14b90520999ec56054 content_type: application/pdf creator: dernst date_created: 2025-01-09T07:56:28Z date_updated: 2025-01-09T07:56:28Z file_id: '18786' file_name: 2024_ReviewsmathPhysics_Henheik.pdf file_size: 503910 relation: main_file success: 1 file_date_updated: 2025-01-09T07:56:28Z has_accepted_license: '1' intvolume: ' 36' isi: 1 issue: '9' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ 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 - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public - id: '18135' relation: dissertation_contains status: public scopus_import: '1' status: public title: Universality in low-dimensional BCS theory 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: 36 year: '2024' ... --- _id: '18107' abstract: - lang: eng text: We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and ρ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260). acknowledgement: 'Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged.' article_number: e78 article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 2024;12. doi:10.1017/fms.2024.56' apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2024.56' chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” Forum of Mathematics, Sigma. Cambridge University Press, 2024. https://doi.org/10.1017/fms.2024.56.' ieee: 'A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” Forum of Mathematics, Sigma, vol. 12. Cambridge University Press, 2024.' ista: 'Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78.' mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” Forum of Mathematics, Sigma, vol. 12, e78, Cambridge University Press, 2024, doi:10.1017/fms.2024.56.' short: A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024). corr_author: '1' date_created: 2024-09-20T12:25:25Z date_published: 2024-09-09T00:00:00Z date_updated: 2026-04-07T13:01:40Z day: '09' ddc: - '510' department: - _id: GradSch - _id: RoSe doi: 10.1017/fms.2024.56 external_id: arxiv: - '2407.05990' isi: - '001307817400001' file: - access_level: open_access checksum: 330b881240013213a8e08538fec13d29 content_type: application/pdf creator: dernst date_created: 2024-09-23T09:56:17Z date_updated: 2024-09-23T09:56:17Z file_id: '18126' file_name: 2024_ForumMath_Lauritsen.pdf file_size: 599886 relation: main_file success: 1 file_date_updated: 2024-09-23T09:56:17Z has_accepted_license: '1' intvolume: ' 12' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '18135' relation: dissertation_contains status: public scopus_import: '1' status: public title: 'Pressure of a dilute spin-polarized Fermi gas: Lower bound' 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 12 year: '2024' ... --- OA_place: publisher _id: '18135' abstract: - lang: eng text: "This thesis consists of two separate parts. In the first part we consider a dilute Fermi gas interacting through a repulsive interaction in dimensions $d=1,2,3$. Our focus is mostly on the physically most relevant dimension $d=3$ \r\nand the setting of a spin-polarized (equivalently spinless) gas, where the Pauli exclusion principle plays a key role. We show that, at zero temperature, the ground state energy density of the interacting spin-polarized gas differs (to leading order) from that of the free (i.e. non-interacting) gas by a term of order $a_p^d\\rho^{2+2/d}$ \ with $a_p$ the $p$-wave scattering length of the repulsive interaction and $\\rho$ the density. Further, we extend this to positive temperature and show that the pressure of an interacting spin-polarized gas differs from that of the free gas by a now temperature dependent term, again of order $a_p^d\\rho^{2+2/d}$. Lastly, we consider the setting of a spin-$\\frac{1}{2}$ Fermi gas in $d=3$ dimensions and show that here, as an upper bound, the ground state energy density differs from that of the free system by a term of order $a_s \\rho^2$ with an error smaller than $a_s \\rho^2 (a_s\\rho^{1/3})^{1-\\eps}$ for any $\\eps > 0$, where $a_s$ is the $s$-wave scattering length of the repulsive interaction. \r\n\r\nThese asymptotic formulas complement the similar formulas in the literature for the dilute Bose and spin-$\\frac{1}{2}$ Fermi gas, where the ground state energies or pressures differ from that of the corresponding free systems by a term of order $a_s \\rho^2$ in dimension $d=3$. In the spin-polarized setting, the corrections, of order $a_p^3\\rho^{8/3}$ in dimension $d=3$, are thus much smaller and requires a more delicate analysis.\r\n\r\nIn the second part of the thesis we consider the Bardeen--Cooper--Schrieffer (BCS) theory of superconductivity and in particular its associated critical temperature and energy gap. We prove that the ratio of the zero-temperature energy gap and critical temperature $\\Xi(T=0)/T_c$ approaches a universal constant $\\pi e^{-\\gamma}\\approx 1.76$ in both the limit of high density in dimension $d=3$ and in the limit of weak coupling in dimensions $d=1,2$. This complements the proofs in the literature of this universal behaviour in the limit of weak coupling or low density in dimension $d=3$. Secondly, we prove that the ratio of the energy gap at positive temperature and critical temperature $\\Xi(T)/T_c$ approaches a universal function of the relative temperature $T/T_c$ in the limit of weak coupling in dimensions $d=1,2,3$." alternative_title: - ISTA Thesis article_processing_charge: No 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. Energies of dilute Fermi gases and universalities in BCS theory. 2024. doi:10.15479/at:ista:18135 apa: Lauritsen, A. B. (2024). Energies of dilute Fermi gases and universalities in BCS theory. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18135 chicago: Lauritsen, Asbjørn Bækgaard. “Energies of Dilute Fermi Gases and Universalities in BCS Theory.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18135. ieee: A. B. Lauritsen, “Energies of dilute Fermi gases and universalities in BCS theory,” Institute of Science and Technology Austria, 2024. ista: Lauritsen AB. 2024. Energies of dilute Fermi gases and universalities in BCS theory. Institute of Science and Technology Austria. mla: Lauritsen, Asbjørn Bækgaard. Energies of Dilute Fermi Gases and Universalities in BCS Theory. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18135. short: A.B. Lauritsen, Energies of Dilute Fermi Gases and Universalities in BCS Theory, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-09-24T10:56:25Z date_published: 2024-09-23T00:00:00Z date_updated: 2026-04-16T08:17:55Z day: '23' ddc: - '515' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:18135 ec_funded: 1 file: - access_level: open_access checksum: c7bc3b31e430d57c65393051ca439575 content_type: application/pdf creator: alaurits date_created: 2024-09-26T13:11:24Z date_updated: 2024-09-26T13:11:24Z file_id: '18147' file_name: Lauritsen-thesis-final.pdf file_size: 3648831 relation: main_file success: 1 - access_level: closed checksum: 39f6b1b7f83e25a3bf9f933f1ea0bc06 content_type: application/x-zip-compressed creator: alaurits date_created: 2024-09-26T13:12:55Z date_updated: 2024-09-26T13:12:55Z file_id: '18148' file_name: Lauritsen-thesis-source.zip file_size: 1625888 relation: source_file file_date_updated: 2024-09-26T13:12:55Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '353' project: - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_identifier: isbn: - 978-3-99078-042-8 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '11732' relation: part_of_dissertation status: public - id: '14542' relation: part_of_dissertation status: public - id: '18107' relation: part_of_dissertation status: public - id: '17240' relation: part_of_dissertation status: public - id: '14931' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Energies of dilute Fermi gases and universalities in BCS theory 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: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- _id: '14931' abstract: - lang: eng text: We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15]. acknowledgement: A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged. article_number: '110320' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 2024;286(7). doi:10.1016/j.jfa.2024.110320' apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110320' chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110320.' ieee: 'A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” Journal of Functional Analysis, vol. 286, no. 7. Elsevier, 2024.' ista: 'Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320.' mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal of Functional Analysis, vol. 286, no. 7, 110320, Elsevier, 2024, doi:10.1016/j.jfa.2024.110320.' short: A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024). corr_author: '1' date_created: 2024-02-04T23:00:53Z date_published: 2024-04-01T00:00:00Z date_updated: 2026-04-16T08:17:56Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1016/j.jfa.2024.110320 ec_funded: 1 external_id: arxiv: - '2301.04894' isi: - '001170294000001' file: - access_level: open_access checksum: ee203cf2dc4420ad90d3c9970d246a78 content_type: application/pdf creator: dernst date_created: 2024-07-22T11:11:56Z date_updated: 2024-07-22T11:11:56Z file_id: '17305' file_name: 2024_JourFunctAnalysis_Lauritsen.pdf file_size: 1381063 relation: main_file success: 1 file_date_updated: 2024-07-22T11:11:56Z has_accepted_license: '1' intvolume: ' 286' isi: 1 issue: '7' language: - iso: eng month: '04' 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: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '18135' relation: dissertation_contains status: public scopus_import: '1' status: public title: 'Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion' 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: ba8df636-2132-11f1-aed0-ed93e2281fdd volume: 286 year: '2024' ... --- _id: '12183' abstract: - lang: eng text: We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit. acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Chiara full_name: Boccato, Chiara id: 342E7E22-F248-11E8-B48F-1D18A9856A87 last_name: Boccato - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 2023;24:1505-1560. doi:10.1007/s00023-022-01252-3 apa: Boccato, C., & Seiringer, R. (2023). The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01252-3 chicago: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01252-3. ieee: C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary conditions,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 1505–1560, 2023. ista: Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 24, 1505–1560. mla: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 1505–60, doi:10.1007/s00023-022-01252-3. short: C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560. corr_author: '1' date_created: 2023-01-15T23:00:52Z date_published: 2023-05-01T00:00:00Z date_updated: 2025-04-14T07:26:59Z day: '01' department: - _id: RoSe doi: 10.1007/s00023-022-01252-3 ec_funded: 1 external_id: arxiv: - '2205.15284' isi: - '000910751800002' intvolume: ' 24' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2205.15284 month: '05' oa: 1 oa_version: Preprint page: 1505-1560 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The Bose Gas in a box with Neumann boundary conditions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 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 arxiv: 1 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). corr_author: '1' date_created: 2023-08-22T14:09:47Z date_published: 2023-07-26T00:00:00Z date_updated: 2024-10-09T21:06:41Z 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: '14254' abstract: - lang: eng text: In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with a much simplified proof. As a corollary we obtain a simple proof of the original Lieb–Thirring inequality. acknowledgement: J.P.S. thanks the Institute of Science and Technology Austria for the hospitality and support during a visit where this work was done. J.P.S. was also partially supported by the VILLUM Centre of Excellence for the Mathematics of Quantum Theory (QMATH) (grant No. 10059). article_number: '110129' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan Philip full_name: Solovej, Jan Philip last_name: Solovej citation: ama: Seiringer R, Solovej JP. A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. 2023;285(10). doi:10.1016/j.jfa.2023.110129 apa: Seiringer, R., & Solovej, J. P. (2023). A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.110129 chicago: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110129. ieee: R. Seiringer and J. P. Solovej, “A simple approach to Lieb-Thirring type inequalities,” Journal of Functional Analysis, vol. 285, no. 10. Elsevier, 2023. ista: Seiringer R, Solovej JP. 2023. A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. 285(10), 110129. mla: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” Journal of Functional Analysis, vol. 285, no. 10, 110129, Elsevier, 2023, doi:10.1016/j.jfa.2023.110129. short: R. Seiringer, J.P. Solovej, Journal of Functional Analysis 285 (2023). corr_author: '1' date_created: 2023-09-03T22:01:14Z date_published: 2023-11-15T00:00:00Z date_updated: 2024-10-09T21:06:47Z day: '15' ddc: - '510' department: - _id: RoSe doi: 10.1016/j.jfa.2023.110129 external_id: arxiv: - '2303.04504' isi: - '001071552300001' file: - access_level: open_access checksum: 28e424ad91be6219e9d321054ce3a412 content_type: application/pdf creator: dernst date_created: 2024-01-30T14:15:16Z date_updated: 2024-01-30T14:15:16Z file_id: '14915' file_name: 2023_JourFunctionalAnalysis_Seiringer.pdf file_size: 232934 relation: main_file success: 1 file_date_updated: 2024-01-30T14:15:16Z has_accepted_license: '1' intvolume: ' 285' isi: 1 issue: '10' language: - iso: eng month: '11' oa: 1 oa_version: Published Version publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: A simple approach to Lieb-Thirring type inequalities 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: 285 year: '2023' ... --- _id: '14441' abstract: - lang: eng text: We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation. acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 2023;404:287-337. doi:10.1007/s00220-023-04841-3' apa: 'Brooks, M., & Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04841-3' chicago: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04841-3.' ieee: 'M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” Communications in Mathematical Physics, vol. 404. Springer Nature, pp. 287–337, 2023.' ista: 'Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337.' mla: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications in Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 287–337, doi:10.1007/s00220-023-04841-3.' short: M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337. corr_author: '1' date_created: 2023-10-22T22:01:13Z date_published: 2023-11-01T00:00:00Z date_updated: 2025-09-09T13:12:02Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00220-023-04841-3 ec_funded: 1 external_id: arxiv: - '2207.03156' isi: - '001096217400007' file: - access_level: open_access checksum: 1ae49b39247cb6b40ff75997381581b8 content_type: application/pdf creator: dernst date_created: 2023-10-31T12:21:39Z date_updated: 2023-10-31T12:21:39Z file_id: '14477' file_name: 2023_CommMathPhysics_Brooks.pdf file_size: 832375 relation: main_file success: 1 file_date_updated: 2023-10-31T12:21:39Z has_accepted_license: '1' intvolume: ' 404' isi: 1 language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 287-337 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body 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: 'The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy' 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 404 year: '2023' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: diamond _id: '14662' abstract: - lang: eng text: We consider a class of polaron models, including the Fröhlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential spectrum. article_processing_charge: Yes article_type: original arxiv: 1 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. Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. 2023;13(3):1045-1055. doi:10.4171/JST/469 apa: Seiringer, R. (2023). Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/469 chicago: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling.” Journal of Spectral Theory. EMS Press, 2023. https://doi.org/10.4171/JST/469. ieee: R. Seiringer, “Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling,” Journal of Spectral Theory, vol. 13, no. 3. EMS Press, pp. 1045–1055, 2023. ista: Seiringer R. 2023. Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. 13(3), 1045–1055. mla: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling.” Journal of Spectral Theory, vol. 13, no. 3, EMS Press, 2023, pp. 1045–55, doi:10.4171/JST/469. short: R. Seiringer, Journal of Spectral Theory 13 (2023) 1045–1055. corr_author: '1' date_created: 2023-12-10T23:00:59Z date_published: 2023-11-25T00:00:00Z date_updated: 2025-09-09T13:40:33Z day: '25' ddc: - '510' department: - _id: RoSe doi: 10.4171/JST/469 external_id: arxiv: - '2210.17123' isi: - '001127467700008' file: - access_level: open_access checksum: 9ce96ca87d56ea9a70d2eb9a32839f8d content_type: application/pdf creator: dernst date_created: 2023-12-11T12:03:12Z date_updated: 2023-12-11T12:03:12Z file_id: '14677' file_name: 2023_JST_Seiringer.pdf file_size: 201513 relation: main_file success: 1 file_date_updated: 2023-12-11T12:03:12Z has_accepted_license: '1' intvolume: ' 13' isi: 1 issue: '3' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 1045-1055 publication: Journal of Spectral Theory publication_identifier: eissn: - 1664-0403 issn: - 1664-039X publication_status: published publisher: EMS Press quality_controlled: '1' scopus_import: '1' status: public title: Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 13 year: '2023' ... --- _id: '14715' abstract: - lang: eng text: We consider N trapped bosons in the mean-field limit with coupling constant λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation. We prove that the probability of finding ℓ particles outside the condensate wave function decays exponentially in ℓ. acknowledgement: We thank Lea Boßmann, Phan Thành Nam and Simone Rademacher for helpful remarks. P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Grant No. SFB/TRR 352 “Mathematics of Many-Body Quantum Systems and Their Collective Phenomena.” article_number: '121901' article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Peter full_name: Pickl, Peter last_name: Pickl citation: ama: Mitrouskas DJ, Pickl P. Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. 2023;64(12). doi:10.1063/5.0172199 apa: Mitrouskas, D. J., & Pickl, P. (2023). Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0172199 chicago: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2023. https://doi.org/10.1063/5.0172199. ieee: D. J. Mitrouskas and P. Pickl, “Exponential decay of the number of excitations in the weakly interacting Bose gas,” Journal of Mathematical Physics, vol. 64, no. 12. AIP Publishing, 2023. ista: Mitrouskas DJ, Pickl P. 2023. Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. 64(12), 121901. mla: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical Physics, vol. 64, no. 12, 121901, AIP Publishing, 2023, doi:10.1063/5.0172199. short: D.J. Mitrouskas, P. Pickl, Journal of Mathematical Physics 64 (2023). corr_author: '1' date_created: 2023-12-31T23:01:02Z date_published: 2023-12-01T00:00:00Z date_updated: 2025-09-09T14:05:28Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1063/5.0172199 external_id: arxiv: - '2307.11062' isi: - '001127432200002' file: - access_level: open_access checksum: 66572f718a36465576cf0d6b3f7e01fc content_type: application/pdf creator: dernst date_created: 2024-01-02T08:45:07Z date_updated: 2024-01-02T08:45:07Z file_id: '14722' file_name: 2023_JourMathPhysics_Mitrouskas.pdf file_size: 4346922 relation: main_file success: 1 file_date_updated: 2024-01-02T08:45:07Z has_accepted_license: '1' intvolume: ' 64' isi: 1 issue: '12' language: - iso: eng month: '12' 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: Exponential decay of the number of excitations in 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 64 year: '2023' ... --- _id: '12430' abstract: - lang: eng text: We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively. article_number: '2350006' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Marco full_name: Falconi, Marco last_name: Falconi - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 citation: ama: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 2023;35(4). doi:10.1142/S0129055X2350006X apa: Falconi, M., Leopold, N. K., Mitrouskas, D. J., & Petrat, S. P. (2023). Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X2350006X chicago: Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” Reviews in Mathematical Physics. World Scientific Publishing, 2023. https://doi.org/10.1142/S0129055X2350006X. ieee: M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov dynamics and higher-order corrections for the regularized Nelson model,” Reviews in Mathematical Physics, vol. 35, no. 4. World Scientific Publishing, 2023. ista: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 35(4), 2350006. mla: Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” Reviews in Mathematical Physics, vol. 35, no. 4, 2350006, World Scientific Publishing, 2023, doi:10.1142/S0129055X2350006X. short: M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical Physics 35 (2023). date_created: 2023-01-29T23:00:59Z date_published: 2023-01-09T00:00:00Z date_updated: 2023-08-16T11:47:27Z day: '09' department: - _id: RoSe doi: 10.1142/S0129055X2350006X external_id: arxiv: - '2110.00458' isi: - '000909760300001' intvolume: ' 35' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2110.00458' month: '01' oa: 1 oa_version: Preprint publication: Reviews in Mathematical Physics publication_identifier: issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Bogoliubov dynamics and higher-order corrections for the regularized Nelson model type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 35 year: '2023' ... --- _id: '12869' abstract: - lang: eng text: 'We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately round cultures get a competitive advantage. We first analyse the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e. freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity and the central European plain has less clear cultural borders. ' acknowledgement: 'FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs. ' article_processing_charge: No author: - first_name: Frederik Ravn full_name: Klausen, Frederik Ravn last_name: Klausen - 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: 'Klausen FR, Lauritsen AB. Research data for: A stochastic cellular automaton model of culture formation. 2023. doi:10.15479/AT:ISTA:12869' apa: 'Klausen, F. R., & Lauritsen, A. B. (2023). Research data for: A stochastic cellular automaton model of culture formation. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:12869' chicago: 'Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Research Data for: A Stochastic Cellular Automaton Model of Culture Formation.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/AT:ISTA:12869.' ieee: 'F. R. Klausen and A. B. Lauritsen, “Research data for: A stochastic cellular automaton model of culture formation.” Institute of Science and Technology Austria, 2023.' ista: 'Klausen FR, Lauritsen AB. 2023. Research data for: A stochastic cellular automaton model of culture formation, Institute of Science and Technology Austria, 10.15479/AT:ISTA:12869.' mla: 'Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. Research Data for: A Stochastic Cellular Automaton Model of Culture Formation. Institute of Science and Technology Austria, 2023, doi:10.15479/AT:ISTA:12869.' short: F.R. Klausen, A.B. Lauritsen, (2023). corr_author: '1' date_created: 2023-04-26T12:34:49Z date_published: 2023-04-26T00:00:00Z date_updated: 2025-09-09T12:26:01Z day: '26' ddc: - '000' department: - _id: GradSch - _id: RoSe doi: 10.15479/AT:ISTA:12869 file: - access_level: open_access checksum: 85ede12d38bb8d944022a8cba4d719f5 content_type: application/octet-stream creator: alaurits date_created: 2023-04-26T12:30:06Z date_updated: 2023-04-26T12:30:06Z file_id: '12870' file_name: README.md file_size: 4567 relation: main_file success: 1 - access_level: open_access checksum: 25bf79452ae895f9c8a20571a096b4c3 content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:27:34Z date_updated: 2023-04-26T12:27:34Z file_id: '12871' file_name: simulations_era=10_flux_varied_europe.zip file_size: 732586731 relation: main_file success: 1 - access_level: open_access checksum: bca48d80ece73eb169aee7211a4a751a content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:29:53Z date_updated: 2023-04-26T12:29:53Z file_id: '12872' file_name: simulations_era=10_flux_varied_torus.zip file_size: 1743893150 relation: main_file success: 1 - access_level: open_access checksum: e77a655db15486a387a36362fbf0b665 content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:29:19Z date_updated: 2023-04-26T12:29:19Z file_id: '12873' file_name: simulations_era=10_R_varied_torus.zip file_size: 878391851 relation: main_file success: 1 - access_level: open_access checksum: 8556406513adc4aa2e0417f46680f627 content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:30:05Z date_updated: 2023-04-26T12:30:05Z file_id: '12874' file_name: simulations_era=100.zip file_size: 201652478 relation: main_file success: 1 file_date_updated: 2023-04-26T12:30:06Z has_accepted_license: '1' license: https://creativecommons.org/publicdomain/zero/1.0/ month: '04' oa: 1 oa_version: Published Version publisher: Institute of Science and Technology Austria related_material: record: - id: '14505' relation: used_in_publication status: deleted - id: '12890' relation: used_in_publication status: public status: public title: 'Research data for: A stochastic cellular automaton model of culture formation' tmp: image: /images/cc_0.png legal_code_url: https://creativecommons.org/publicdomain/zero/1.0/legalcode name: Creative Commons Public Domain Dedication (CC0 1.0) short: CC0 (1.0) type: research_data user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '12890' abstract: - lang: eng text: We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately geometrically round cultures get a competitive advantage. We first analyze the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e., freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely, that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity, and the central European plain has less clear cultural borders. acknowledgement: Thanks to Kim Sneppen, Svend Krøjer, Peter Wildemann, Peter Rasmussen and Kent Bækgaard Lauritsen for discussions and suggestions. FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs. article_number: '054307' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Frederik Ravn full_name: Klausen, Frederik Ravn last_name: Klausen - 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: Klausen FR, Lauritsen AB. Stochastic cellular automaton model of culture formation. Physical Review E. 2023;108(5). doi:10.1103/PhysRevE.108.054307 apa: Klausen, F. R., & Lauritsen, A. B. (2023). Stochastic cellular automaton model of culture formation. Physical Review E. American Physical Society. https://doi.org/10.1103/PhysRevE.108.054307 chicago: Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” Physical Review E. American Physical Society, 2023. https://doi.org/10.1103/PhysRevE.108.054307. ieee: F. R. Klausen and A. B. Lauritsen, “Stochastic cellular automaton model of culture formation,” Physical Review E, vol. 108, no. 5. American Physical Society, 2023. ista: Klausen FR, Lauritsen AB. 2023. Stochastic cellular automaton model of culture formation. Physical Review E. 108(5), 054307. mla: Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” Physical Review E, vol. 108, no. 5, 054307, American Physical Society, 2023, doi:10.1103/PhysRevE.108.054307. short: F.R. Klausen, A.B. Lauritsen, Physical Review E 108 (2023). corr_author: '1' date_created: 2023-05-04T08:35:01Z date_published: 2023-11-08T00:00:00Z date_updated: 2025-09-09T12:26:01Z day: '08' department: - _id: GradSch - _id: RoSe doi: 10.1103/PhysRevE.108.054307 external_id: arxiv: - '2305.02153' isi: - '001106396300005' pmid: - '38115445' intvolume: ' 108' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2305.02153 month: '11' oa: 1 oa_version: Preprint pmid: 1 publication: Physical Review E publication_identifier: eissn: - 2470-0053 issn: - 2470-0045 publication_status: published publisher: American Physical Society quality_controlled: '1' related_material: link: - relation: software url: https://github.com/FrederikRavnKlausen/model-for-culture-formation record: - id: '12869' relation: research_data status: public scopus_import: '1' status: public title: Stochastic cellular automaton model of culture formation type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 108 year: '2023' ... --- _id: '12911' abstract: - lang: eng text: 'This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.' acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813." article_number: '109963' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963 apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963 chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023. ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963. mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963. short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023). date_created: 2023-05-07T22:01:02Z date_published: 2023-08-15T00:00:00Z date_updated: 2025-04-15T08:31:52Z day: '15' department: - _id: RoSe - _id: JaMa doi: 10.1016/j.jfa.2023.109963 ec_funded: 1 external_id: arxiv: - '2106.11217' isi: - '000990804300001' intvolume: ' 285' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '08' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: F06504 name: Taming Complexity in Partial Differential Systems publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '9792' relation: earlier_version status: public scopus_import: '1' status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '13178' abstract: - lang: eng text: We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar. acknowledgement: This research was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.). article_processing_charge: Yes article_type: original arxiv: 1 author: - 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 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. 2023;11:1-52. doi:10.1017/fms.2023.45 apa: Mitrouskas, D. J., Mysliwy, K., & Seiringer, R. (2023). Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. Cambridge University Press. https://doi.org/10.1017/fms.2023.45 chicago: Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” Forum of Mathematics. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.45. ieee: D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron,” Forum of Mathematics, vol. 11. Cambridge University Press, pp. 1–52, 2023. ista: Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. 11, 1–52. mla: Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” Forum of Mathematics, vol. 11, Cambridge University Press, 2023, pp. 1–52, doi:10.1017/fms.2023.45. short: D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023) 1–52. corr_author: '1' date_created: 2023-07-02T22:00:43Z date_published: 2023-06-13T00:00:00Z date_updated: 2025-04-14T07:26:58Z day: '13' ddc: - '500' department: - _id: RoSe doi: 10.1017/fms.2023.45 ec_funded: 1 external_id: arxiv: - '2203.02454' isi: - '001005008800001' file: - access_level: open_access checksum: f672eb7dd015c472c9a04f1b9bf9df7d content_type: application/pdf creator: alisjak date_created: 2023-07-03T10:36:25Z date_updated: 2023-07-03T10:36:25Z file_id: '13186' file_name: 2023_ForumofMathematics.Sigma_Mitrouskas.pdf file_size: 943192 relation: main_file success: 1 file_date_updated: 2023-07-03T10:36:25Z has_accepted_license: '1' intvolume: ' 11' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1-52 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Forum of Mathematics publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '13225' abstract: - lang: eng text: Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy. acknowledgement: "RS was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227). MP acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement." article_number: '65' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Niels P full_name: Benedikter, Niels P id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87 last_name: Benedikter orcid: 0000-0002-1071-6091 - first_name: Marcello full_name: Porta, Marcello last_name: Porta - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 2023;247(4). doi:10.1007/s00205-023-01893-6 apa: Benedikter, N. P., Porta, M., Schlein, B., & Seiringer, R. (2023). Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01893-6 chicago: Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” Archive for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01893-6. ieee: N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas with large interaction potential,” Archive for Rational Mechanics and Analysis, vol. 247, no. 4. Springer Nature, 2023. ista: Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 247(4), 65. mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” Archive for Rational Mechanics and Analysis, vol. 247, no. 4, 65, Springer Nature, 2023, doi:10.1007/s00205-023-01893-6. short: N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023). date_created: 2023-07-16T22:01:08Z date_published: 2023-08-01T00:00:00Z date_updated: 2025-04-14T07:26:58Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00205-023-01893-6 ec_funded: 1 external_id: arxiv: - '2106.13185' isi: - '001024369000001' file: - access_level: open_access checksum: 2b45828d854a253b14bf7aa196ec55e9 content_type: application/pdf creator: dernst date_created: 2023-11-14T13:12:12Z date_updated: 2023-11-14T13:12:12Z file_id: '14535' file_name: 2023_ArchiveRationalMechAnalysis_Benedikter.pdf file_size: 851626 relation: main_file success: 1 file_date_updated: 2023-11-14T13:12:12Z has_accepted_license: '1' intvolume: ' 247' isi: 1 issue: '4' language: - iso: eng month: '08' 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 publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Correlation energy of a weakly interacting Fermi gas with large interaction potential 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: 247 year: '2023' ... --- OA_place: publisher OA_type: hybrid _id: '13226' abstract: - lang: eng text: We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion. acknowledgement: "It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee for many constructive comments. L.B. gratefully acknowledges funding from the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111) and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen Access funding enabled and organized by Projekt DEAL." article_number: '77' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Lea full_name: Bossmann, Lea id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425 last_name: Bossmann orcid: 0000-0002-6854-1343 - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 citation: ama: Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 2023;113(4). doi:10.1007/s11005-023-01698-4 apa: Bossmann, L., & Petrat, S. P. (2023). Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-023-01698-4 chicago: Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” Letters in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s11005-023-01698-4. ieee: L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field Bose gas,” Letters in Mathematical Physics, vol. 113, no. 4. Springer Nature, 2023. ista: Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77. mla: Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” Letters in Mathematical Physics, vol. 113, no. 4, 77, Springer Nature, 2023, doi:10.1007/s11005-023-01698-4. short: L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023). corr_author: '1' date_created: 2023-07-16T22:01:08Z date_published: 2023-07-03T00:00:00Z date_updated: 2025-06-25T06:20:15Z day: '03' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-023-01698-4 ec_funded: 1 external_id: arxiv: - '2208.00199' isi: - '001022878900002' file: - access_level: open_access checksum: 995c902a989a6769fd3db456cfd41111 content_type: application/pdf creator: dernst date_created: 2025-06-25T06:20:02Z date_updated: 2025-06-25T06:20:02Z file_id: '19898' file_name: 2023_LettersMathPhysics_Bossmann.pdf file_size: 586698 relation: main_file success: 1 file_date_updated: 2025-06-25T06:20:02Z has_accepted_license: '1' intvolume: ' 113' isi: 1 issue: '4' language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships 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: Weak Edgeworth expansion for the mean-field 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 113 year: '2023' ... --- OA_place: repository OA_type: green _id: '14854' abstract: - lang: eng text: We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math. Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov type. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Mitrouskas DJ, Seiringer R. Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. 2023;5(4):973-1008. doi:10.2140/paa.2023.5.973 apa: Mitrouskas, D. J., & Seiringer, R. (2023). Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2023.5.973 chicago: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States for the Strongly Coupled Polaron.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/paa.2023.5.973. ieee: D. J. Mitrouskas and R. Seiringer, “Ubiquity of bound states for the strongly coupled polaron,” Pure and Applied Analysis, vol. 5, no. 4. Mathematical Sciences Publishers, pp. 973–1008, 2023. ista: Mitrouskas DJ, Seiringer R. 2023. Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. 5(4), 973–1008. mla: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States for the Strongly Coupled Polaron.” Pure and Applied Analysis, vol. 5, no. 4, Mathematical Sciences Publishers, 2023, pp. 973–1008, doi:10.2140/paa.2023.5.973. short: D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008. corr_author: '1' date_created: 2024-01-22T08:24:23Z date_published: 2023-12-15T00:00:00Z date_updated: 2025-04-23T14:21:39Z day: '15' department: - _id: RoSe doi: 10.2140/paa.2023.5.973 external_id: arxiv: - '2211.03606' intvolume: ' 5' issue: '4' keyword: - General Medicine language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2211.03606 month: '12' oa: 1 oa_version: Preprint page: 973-1008 publication: Pure and Applied Analysis publication_identifier: eissn: - 2578-5885 issn: - 2578-5893 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Ubiquity of bound states for the strongly coupled polaron type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 5 year: '2023' ... --- _id: '14992' abstract: - lang: eng text: In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of this functional, corresponding to using mixed canonical and grand-canonical states, respectively. We present some recent works about the local density approximation, in which the functionals get replaced by purely local functionals constructed using the uniform electron gas energy per unit volume. We then review the known upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic energy alone, then turn to the classical interaction alone, before we are able to put everything together. A later section is devoted to the Hohenberg–Kohn theorem and the role of many-body unique continuation in its proof. alternative_title: - Mathematics and Molecular Modeling article_processing_charge: No arxiv: 1 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. Universal Functionals in Density Functional Theory. In: Cances E, Friesecke G, eds. Density Functional Theory. 1st ed. MAMOMO. Springer; 2023:115-182. doi:10.1007/978-3-031-22340-2_3' apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2023). Universal Functionals in Density Functional Theory. In E. Cances & G. Friesecke (Eds.), Density Functional Theory (1st ed., pp. 115–182). Springer. https://doi.org/10.1007/978-3-031-22340-2_3 chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Universal Functionals in Density Functional Theory.” In Density Functional Theory, edited by Eric Cances and Gero Friesecke, 1st ed., 115–82. MAMOMO. Springer, 2023. https://doi.org/10.1007/978-3-031-22340-2_3. ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Universal Functionals in Density Functional Theory,” in Density Functional Theory, 1st ed., E. Cances and G. Friesecke, Eds. Springer, 2023, pp. 115–182. ista: 'Lewin M, Lieb EH, Seiringer R. 2023.Universal Functionals in Density Functional Theory. In: Density Functional Theory. Mathematics and Molecular Modeling, , 115–182.' mla: Lewin, Mathieu, et al. “Universal Functionals in Density Functional Theory.” Density Functional Theory, edited by Eric Cances and Gero Friesecke, 1st ed., Springer, 2023, pp. 115–82, doi:10.1007/978-3-031-22340-2_3. short: M. Lewin, E.H. Lieb, R. Seiringer, in:, E. Cances, G. Friesecke (Eds.), Density Functional Theory, 1st ed., Springer, 2023, pp. 115–182. date_created: 2024-02-14T14:44:33Z date_published: 2023-07-19T00:00:00Z date_updated: 2024-02-20T08:33:06Z day: '19' department: - _id: RoSe doi: 10.1007/978-3-031-22340-2_3 edition: '1' editor: - first_name: Eric full_name: Cances, Eric last_name: Cances - first_name: Gero full_name: Friesecke, Gero last_name: Friesecke external_id: arxiv: - '1912.10424' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1912.10424 month: '07' oa: 1 oa_version: Preprint page: 115-182 publication: Density Functional Theory publication_identifier: eisbn: - '9783031223402' isbn: - '9783031223396' issn: - 3005-0286 publication_status: published publisher: Springer quality_controlled: '1' series_title: MAMOMO status: public title: Universal Functionals in Density Functional Theory type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '17074' abstract: - lang: eng text: We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy EN is given by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states ΨN, i.e. states satisfying ⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect to one of the Hartree minimizers. acknowledgement: "We are grateful to Rupert Frank for helpful discussions at an early stage of this project.\r\nFunding from the European Union’s Horizon 2020 research and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. 2023;3(4):939-1000. doi:10.2140/pmp.2022.3.939 apa: Brooks, M., & Seiringer, R. (2023). Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2022.3.939 chicago: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pmp.2022.3.939. ieee: M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases,” Probability and Mathematical Physics, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 939–1000, 2023. ista: Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. 3(4), 939–1000. mla: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” Probability and Mathematical Physics, vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:10.2140/pmp.2022.3.939. short: M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000. corr_author: '1' date_created: 2024-05-29T06:12:54Z date_published: 2023-02-21T00:00:00Z date_updated: 2025-04-14T07:26:59Z day: '21' department: - _id: RoSe doi: 10.2140/pmp.2022.3.939 ec_funded: 1 external_id: arxiv: - '2111.13864' intvolume: ' 3' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2111.13864 month: '02' oa: 1 oa_version: Preprint page: 939-1000 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Probability and Mathematical Physics publication_identifier: eissn: - 2690-1005 issn: - 2690-0998 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 3 year: '2023' ...