[{"status":"public","article_number":"20","date_published":"2025-04-01T00:00:00Z","title":"BCS critical temperature on half-spaces","external_id":{"arxiv":["2306.05824"],"pmid":["40041541"],"isi":["001435380100001"]},"author":[{"last_name":"Roos","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","first_name":"Barbara"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert"}],"citation":{"short":"B. Roos, R. Seiringer, Archive for Rational Mechanics and Analysis 249 (2025).","mla":"Roos, Barbara, and Robert Seiringer. “BCS Critical Temperature on Half-Spaces.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, 20, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00205-025-02088-x\">10.1007/s00205-025-02088-x</a>.","chicago":"Roos, Barbara, and Robert Seiringer. “BCS Critical Temperature on Half-Spaces.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00205-025-02088-x\">https://doi.org/10.1007/s00205-025-02088-x</a>.","ieee":"B. Roos and R. Seiringer, “BCS critical temperature on half-spaces,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249. Springer Nature, 2025.","apa":"Roos, B., &#38; Seiringer, R. (2025). BCS critical temperature on half-spaces. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-025-02088-x\">https://doi.org/10.1007/s00205-025-02088-x</a>","ista":"Roos B, Seiringer R. 2025. BCS critical temperature on half-spaces. Archive for Rational Mechanics and Analysis. 249, 20.","ama":"Roos B, Seiringer R. BCS critical temperature on half-spaces. <i>Archive for Rational Mechanics and Analysis</i>. 2025;249. doi:<a href=\"https://doi.org/10.1007/s00205-025-02088-x\">10.1007/s00205-025-02088-x</a>"},"publisher":"Springer Nature","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","OA_place":"publisher","doi":"10.1007/s00205-025-02088-x","pmid":1,"department":[{"_id":"RoSe"}],"ddc":["510"],"type":"journal_article","abstract":[{"lang":"eng","text":"We study the BCS critical temperature on half-spaces in dimensions d =1, 2, 3 with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on Rd, at least at weak coupling in d = 1, 2 and weak coupling and small chemical potential in d = 3. Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit."}],"article_type":"original","OA_type":"hybrid","publication":"Archive for Rational Mechanics and Analysis","month":"04","quality_controlled":"1","arxiv":1,"volume":249,"date_updated":"2025-09-30T11:01:08Z","publication_status":"published","file_date_updated":"2025-03-17T10:07:45Z","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged.","has_accepted_license":"1","file":[{"content_type":"application/pdf","checksum":"66803fb63a57987eb4f13ee2949bea77","access_level":"open_access","date_created":"2025-03-17T10:07:45Z","file_size":1224282,"relation":"main_file","file_id":"19412","creator":"dernst","success":1,"date_updated":"2025-03-17T10:07:45Z","file_name":"2025_ArchiveRatMech_Roos.pdf"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"corr_author":"1","day":"01","_id":"19403","language":[{"iso":"eng"}],"intvolume":"       249","year":"2025","date_created":"2025-03-16T23:01:24Z","isi":1,"project":[{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"article_processing_charge":"Yes (via OA deal)","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"license":"https://creativecommons.org/licenses/by/4.0/","scopus_import":"1"},{"year":"2025","date_created":"2025-05-11T22:02:37Z","isi":1,"day":"01","_id":"19660","language":[{"iso":"eng"}],"intvolume":"       249","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"relation":"main_file","file_size":886318,"date_created":"2025-05-12T07:27:28Z","access_level":"open_access","content_type":"application/pdf","checksum":"3606ebd34d59d03f8c66a3a1794c3e4f","file_name":"2025_ArchiveRatioMechanics_Mitrouskas.pdf","date_updated":"2025-05-12T07:27:28Z","creator":"dernst","success":1,"file_id":"19676"}],"corr_author":"1","issue":"3","scopus_import":"1","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"article_processing_charge":"Yes (via OA deal)","ddc":["530"],"department":[{"_id":"RoSe"}],"abstract":[{"lang":"eng","text":"We analyze the ground state energy of N fermions in a two-dimensional box interacting with an impurity particle via two-body point interactions. We show that for weak coupling, the ground state energy is asymptotically described by the polaron energy, as proposed by F. Chevy in the physics literature. The polaron energy is the solution of a nonlinear equation involving the Green’s function of the free Fermi gas and the binding energy of the two-body point interaction. We provide quantitative error estimates that are uniform in the thermodynamic limit."}],"type":"journal_article","article_type":"original","OA_type":"hybrid","article_number":"30","title":"The weakly coupled two-dimensional Fermi polaron","date_published":"2025-06-01T00:00:00Z","external_id":{"isi":["001482770500001"]},"status":"public","oa_version":"Published Version","OA_place":"publisher","doi":"10.1007/s00205-025-02098-9","author":[{"full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","last_name":"Mitrouskas"}],"publisher":"Springer Nature","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00205-025-02098-9\">https://doi.org/10.1007/s00205-025-02098-9</a>.","short":"D.J. Mitrouskas, Archive for Rational Mechanics and Analysis 249 (2025).","mla":"Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, no. 3, 30, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00205-025-02098-9\">10.1007/s00205-025-02098-9</a>.","ama":"Mitrouskas DJ. The weakly coupled two-dimensional Fermi polaron. <i>Archive for Rational Mechanics and Analysis</i>. 2025;249(3). doi:<a href=\"https://doi.org/10.1007/s00205-025-02098-9\">10.1007/s00205-025-02098-9</a>","apa":"Mitrouskas, D. J. (2025). The weakly coupled two-dimensional Fermi polaron. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-025-02098-9\">https://doi.org/10.1007/s00205-025-02098-9</a>","ista":"Mitrouskas DJ. 2025. The weakly coupled two-dimensional Fermi polaron. Archive for Rational Mechanics and Analysis. 249(3), 30.","ieee":"D. J. Mitrouskas, “The weakly coupled two-dimensional Fermi polaron,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, no. 3. Springer Nature, 2025."},"file_date_updated":"2025-05-12T07:27:28Z","oa":1,"publication_status":"published","has_accepted_license":"1","acknowledgement":"The author would like to thank Ulrich Linden for introducing him to the Fermi polaron and for his valuable contributions in the early stages of this project. Additionally, the author is grateful to Krzysztof Myśliwy for helpful comments. Open access funding provided by Institute of Science and Technology (IST Austria).","month":"06","quality_controlled":"1","publication":"Archive for Rational Mechanics and Analysis","date_updated":"2025-09-30T12:25:19Z","volume":249},{"volume":248,"date_updated":"2025-09-08T09:11:41Z","publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"month":"09","quality_controlled":"1","has_accepted_license":"1","acknowledgement":"J. Fischer and M. Moser have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819).\r\nOpen Access funding enabled and organized by Projekt DEAL.","publication_status":"published","oa":1,"file_date_updated":"2024-09-09T08:43:32Z","publisher":"Springer Nature","citation":{"ama":"Abels H, Fischer JL, Moser M. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. <i>Archive for Rational Mechanics and Analysis</i>. 2024;248(5). doi:<a href=\"https://doi.org/10.1007/s00205-024-02020-9\">10.1007/s00205-024-02020-9</a>","apa":"Abels, H., Fischer, J. L., &#38; Moser, M. (2024). Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-024-02020-9\">https://doi.org/10.1007/s00205-024-02020-9</a>","ista":"Abels H, Fischer JL, Moser M. 2024. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive for Rational Mechanics and Analysis. 248(5), 77.","ieee":"H. Abels, J. L. Fischer, and M. Moser, “Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 248, no. 5. Springer Nature, 2024.","chicago":"Abels, Helmut, Julian L Fischer, and Maximilian Moser. “Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00205-024-02020-9\">https://doi.org/10.1007/s00205-024-02020-9</a>.","mla":"Abels, Helmut, et al. “Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 248, no. 5, 77, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00205-024-02020-9\">10.1007/s00205-024-02020-9</a>.","short":"H. Abels, J.L. Fischer, M. Moser, Archive for Rational Mechanics and Analysis 248 (2024)."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"full_name":"Abels, Helmut","first_name":"Helmut","last_name":"Abels"},{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L"},{"full_name":"Moser, Maximilian","first_name":"Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser"}],"doi":"10.1007/s00205-024-02020-9","pmid":1,"oa_version":"Published Version","status":"public","external_id":{"pmid":["39239088"],"isi":["001305530600001"],"arxiv":["2311.02997"]},"title":"Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system","date_published":"2024-09-03T00:00:00Z","article_number":"77","article_type":"original","type":"journal_article","abstract":[{"lang":"eng","text":"We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility  mε>0  in the Allen-Cahn equation tends to zero in a subcritical way, i.e.,  mε=m0εβ  for some  β∈(0,2)  and  m0>0 . The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term  mεHΓt  in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow."}],"ddc":["510"],"department":[{"_id":"JuFi"}],"article_processing_charge":"Yes (via OA deal)","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"scopus_import":"1","issue":"5","ec_funded":1,"file":[{"file_size":811131,"date_created":"2024-09-09T08:43:32Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"98493a05b84e4513b6394dfad4851ddf","file_name":"2024_ArchiveRatAnalysis_Abels.pdf","success":1,"file_id":"17938","creator":"dernst","date_updated":"2024-09-09T08:43:32Z"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"_id":"17887","intvolume":"       248","day":"03","isi":1,"date_created":"2024-09-08T22:01:10Z","year":"2024"},{"status":"public","title":"Correlation energy of a weakly interacting Fermi gas with large interaction potential","article_number":"65","date_published":"2023-08-01T00:00:00Z","external_id":{"arxiv":["2106.13185"],"isi":["001024369000001"]},"author":[{"first_name":"Niels P","full_name":"Benedikter, Niels P","orcid":"0000-0002-1071-6091","last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"}],"citation":{"short":"N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023).","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4, 65, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>.","chicago":"Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>.","ieee":"N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas with large interaction potential,” <i>Archive for Rational Mechanics and Analysis</i>, 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.","apa":"Benedikter, N. P., Porta, M., Schlein, B., &#38; Seiringer, R. (2023). Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>","ama":"Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(4). doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>"},"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","doi":"10.1007/s00205-023-01893-6","ddc":["510"],"department":[{"_id":"RoSe"}],"type":"journal_article","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."}],"article_type":"original","publication":"Archive for Rational Mechanics and Analysis","month":"08","quality_controlled":"1","arxiv":1,"volume":247,"date_updated":"2025-04-14T07:26:58Z","publication_status":"published","file_date_updated":"2023-11-14T13:12:12Z","oa":1,"has_accepted_license":"1","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.","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_name":"2023_ArchiveRationalMechAnalysis_Benedikter.pdf","date_updated":"2023-11-14T13:12:12Z","creator":"dernst","file_id":"14535","success":1,"relation":"main_file","file_size":851626,"date_created":"2023-11-14T13:12:12Z","access_level":"open_access","checksum":"2b45828d854a253b14bf7aa196ec55e9","content_type":"application/pdf"}],"day":"01","_id":"13225","intvolume":"       247","language":[{"iso":"eng"}],"date_created":"2023-07-16T22:01:08Z","year":"2023","isi":1,"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"Yes (via OA deal)","ec_funded":1,"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"issue":"4","scopus_import":"1"},{"article_processing_charge":"No","extern":"1","issue":"4","scopus_import":"1","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"day":"16","_id":"10174","intvolume":"       247","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2104.04263","open_access":"1"}],"year":"2023","date_created":"2021-10-23T10:50:55Z","date_updated":"2025-01-20T14:44:10Z","volume":247,"quality_controlled":"1","month":"07","arxiv":1,"publication":"Archive for Rational Mechanics and Analysis ","acknowledgement":"The authors warmly thank Mitia Duerinckx for discussions on annealed estimates, and Mathias Schäffner for pointing out that the conditions of [14] apply to  ̄a in the setting of Theorem 2.2 and for discussions on regularity theory for operators with non-standard growth conditions. The authors received financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement n◦ 864066).","oa":1,"publication_status":"draft","oa_version":"Preprint","doi":"10.1007/s00205-023-01895-4","author":[{"full_name":"Clozeau, Nicolas","first_name":"Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","last_name":"Clozeau"},{"last_name":"Gloria","full_name":"Gloria, Antoine","first_name":"Antoine"}],"citation":{"ama":"Clozeau N, Gloria A. Quantitative nonlinear homogenization: Control of oscillations. <i>Archive for Rational Mechanics and Analysis </i>. 247(4). doi:<a href=\"https://doi.org/10.1007/s00205-023-01895-4\">10.1007/s00205-023-01895-4</a>","apa":"Clozeau, N., &#38; Gloria, A. (n.d.). Quantitative nonlinear homogenization: Control of oscillations. <i>Archive for Rational Mechanics and Analysis </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01895-4\">https://doi.org/10.1007/s00205-023-01895-4</a>","ista":"Clozeau N, Gloria A. Quantitative nonlinear homogenization: Control of oscillations. Archive for Rational Mechanics and Analysis . 247(4), 67.","ieee":"N. Clozeau and A. Gloria, “Quantitative nonlinear homogenization: Control of oscillations,” <i>Archive for Rational Mechanics and Analysis </i>, vol. 247, no. 4. Springer Nature.","chicago":"Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization: Control of Oscillations.” <i>Archive for Rational Mechanics and Analysis </i>. Springer Nature, n.d. <a href=\"https://doi.org/10.1007/s00205-023-01895-4\">https://doi.org/10.1007/s00205-023-01895-4</a>.","mla":"Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization: Control of Oscillations.” <i>Archive for Rational Mechanics and Analysis </i>, vol. 247, no. 4, 67, Springer Nature, doi:<a href=\"https://doi.org/10.1007/s00205-023-01895-4\">10.1007/s00205-023-01895-4</a>.","short":"N. Clozeau, A. Gloria, Archive for Rational Mechanics and Analysis  247 (n.d.)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","date_published":"2023-07-16T00:00:00Z","title":"Quantitative nonlinear homogenization: Control of oscillations","article_number":"67","external_id":{"arxiv":["2104.04263"]},"status":"public","article_type":"original","OA_type":"green","type":"journal_article","abstract":[{"lang":"eng","text":"Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting of monotone operators with p-growth. This first work is dedicated to a quantitative two-scale expansion result. Fluctuations will be addressed in companion articles. By treating the range of exponents 2≤p<∞ in dimensions d≤3, we are able to consider genuinely nonlinear elliptic equations and systems such as −∇⋅A(x)(1+|∇u|p−2)∇u=f (with A random, non-necessarily symmetric) for the first time. When going from p=2 to p>2, the main difficulty is to analyze the associated linearized operator, whose coefficients are degenerate, unbounded, and depend on the random input A via the solution of a nonlinear equation. One of our main achievements is the control of this intricate nonlinear dependence, leading to annealed Meyers' estimates for the linearized operator, which are key to the quantitative two-scale expansion result."}]},{"article_type":"original","ddc":["510"],"department":[{"_id":"JuFi"}],"abstract":[{"lang":"eng","text":"The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1  (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles."}],"type":"journal_article","author":[{"orcid":"0000-0002-6269-5149","last_name":"Cornalba","id":"2CEB641C-A400-11E9-A717-D712E6697425","full_name":"Cornalba, Federico","first_name":"Federico"},{"last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","first_name":"Julian L","full_name":"Fischer, Julian L"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023).","mla":"Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 5, 76, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01903-7\">10.1007/s00205-023-01903-7</a>.","chicago":"Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01903-7\">https://doi.org/10.1007/s00205-023-01903-7</a>.","apa":"Cornalba, F., &#38; Fischer, J. L. (2023). The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01903-7\">https://doi.org/10.1007/s00205-023-01903-7</a>","ista":"Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 247(5), 76.","ieee":"F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 5. Springer Nature, 2023.","ama":"Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(5). doi:<a href=\"https://doi.org/10.1007/s00205-023-01903-7\">10.1007/s00205-023-01903-7</a>"},"publisher":"Springer Nature","oa_version":"Published Version","doi":"10.1007/s00205-023-01903-7","pmid":1,"status":"public","date_published":"2023-08-04T00:00:00Z","article_number":"76","title":"The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles","external_id":{"isi":["001043086800001"],"pmid":["37547904"],"arxiv":["2109.06500"]},"has_accepted_license":"1","acknowledgement":"We thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science Fund (FWF).","publication_status":"published","file_date_updated":"2024-01-30T12:09:34Z","oa":1,"volume":247,"date_updated":"2025-04-23T13:06:01Z","publication":"Archive for Rational Mechanics and Analysis","month":"08","quality_controlled":"1","arxiv":1,"isi":1,"year":"2023","date_created":"2021-12-16T12:16:03Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_name":"2023_ArchiveRationalMech_Cornalba.pdf","date_updated":"2024-01-30T12:09:34Z","success":1,"file_id":"14904","creator":"dernst","relation":"main_file","date_created":"2024-01-30T12:09:34Z","file_size":1851185,"access_level":"open_access","content_type":"application/pdf","checksum":"4529eeff170b6745a461d397ee611b5a"}],"corr_author":"1","day":"04","_id":"10551","intvolume":"       247","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"issue":"5","scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}]},{"abstract":[{"lang":"eng","text":"We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging."}],"type":"journal_article","department":[{"_id":"RoSe"}],"ddc":["530"],"page":"1835–1906","article_type":"original","external_id":{"arxiv":["2101.12566"],"isi":["000710850600001"]},"date_published":"2021-10-25T00:00:00Z","title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics","status":"public","doi":"10.1007/s00205-021-01715-7","oa_version":"Published Version","citation":{"chicago":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01715-7\">https://doi.org/10.1007/s00205-021-01715-7</a>.","mla":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906, doi:<a href=\"https://doi.org/10.1007/s00205-021-01715-7\">10.1007/s00205-021-01715-7</a>.","short":"D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis 242 (2021) 1835–1906.","ama":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. <i>Archive for Rational Mechanics and Analysis</i>. 2021;242(3):1835–1906. doi:<a href=\"https://doi.org/10.1007/s00205-021-01715-7\">10.1007/s00205-021-01715-7</a>","ieee":"D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.","ista":"Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 242(3), 1835–1906.","apa":"Feliciangeli, D., &#38; Seiringer, R. (2021). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01715-7\">https://doi.org/10.1007/s00205-021-01715-7</a>"},"publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","first_name":"Dario","full_name":"Feliciangeli, Dario"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert"}],"oa":1,"file_date_updated":"2021-12-14T08:35:42Z","publication_status":"published","has_accepted_license":"1","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. We would also like to thank Rupert Frank for many helpful discussions, especially related to the Gross coordinate transformation defined in Def. 4.7.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","arxiv":1,"quality_controlled":"1","month":"10","publication":"Archive for Rational Mechanics and Analysis","date_updated":"2025-04-14T09:11:09Z","volume":242,"year":"2021","date_created":"2021-11-07T23:01:26Z","isi":1,"language":[{"iso":"eng"}],"_id":"10224","intvolume":"       242","day":"25","related_material":{"record":[{"id":"9787","status":"public","relation":"earlier_version"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_name":"2021_Springer_Feliciangeli.pdf","file_id":"10544","creator":"alisjak","success":1,"date_updated":"2021-12-14T08:35:42Z","date_created":"2021-12-14T08:35:42Z","file_size":990529,"relation":"main_file","checksum":"672e9c21b20f1a50854b7c821edbb92f","content_type":"application/pdf","access_level":"open_access"}],"ec_funded":1,"scopus_import":"1","issue":"3","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"article_processing_charge":"Yes (via OA deal)"},{"publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"month":"06","quality_controlled":"1","volume":242,"date_updated":"2023-08-17T06:23:21Z","publication_status":"published","oa":1,"file_date_updated":"2021-12-16T14:58:08Z","has_accepted_license":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441.","status":"public","external_id":{"isi":["000668431200001"],"arxiv":["1908.02273"]},"title":"Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems","date_published":"2021-06-30T00:00:00Z","publisher":"Springer Nature","citation":{"chicago":"Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01686-9\">https://doi.org/10.1007/s00205-021-01686-9</a>.","mla":"Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:<a href=\"https://doi.org/10.1007/s00205-021-01686-9\">10.1007/s00205-021-01686-9</a>.","short":"J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452.","ama":"Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational Mechanics and Analysis</i>. 2021;242(1):343-452. doi:<a href=\"https://doi.org/10.1007/s00205-021-01686-9\">10.1007/s00205-021-01686-9</a>","ieee":"J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021.","ista":"Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452.","apa":"Fischer, J. L., &#38; Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01686-9\">https://doi.org/10.1007/s00205-021-01686-9</a>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","full_name":"Fischer, Julian L","first_name":"Julian L"},{"last_name":"Neukamm","first_name":"Stefan","full_name":"Neukamm, Stefan"}],"doi":"10.1007/s00205-021-01686-9","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \\mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \\varepsilon >0, we establish homogenization error estimates of the order \\varepsilon in case d\\geqq 3, and of the order \\varepsilon |\\log \\varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \\varepsilon ^\\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\\alpha } regularity theory is available."}],"type":"journal_article","ddc":["530"],"department":[{"_id":"JuFi"}],"page":"343-452","article_type":"original","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"scopus_import":"1","issue":"1","file":[{"file_name":"2021_ArchRatMechAnalysis_Fischer.pdf","creator":"cchlebak","file_id":"10558","success":1,"date_updated":"2021-12-16T14:58:08Z","date_created":"2021-12-16T14:58:08Z","file_size":1640121,"relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"cc830b739aed83ca2e32c4e0ce266a4c"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"intvolume":"       242","_id":"10549","language":[{"iso":"eng"}],"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"day":"30","year":"2021","date_created":"2021-12-16T12:12:33Z","isi":1},{"scopus_import":"1","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"ec_funded":1,"article_processing_charge":"No","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"isi":1,"year":"2021","date_created":"2021-03-14T23:01:34Z","_id":"9246","intvolume":"       240","language":[{"iso":"eng"}],"day":"26","file":[{"file_name":"2021_ArchRationalMechAnal_Leopold.pdf","date_updated":"2021-03-22T08:31:29Z","success":1,"file_id":"9270","creator":"dernst","relation":"main_file","date_created":"2021-03-22T08:31:29Z","file_size":558006,"checksum":"23449e44dc5132501a5c86e70638800f","content_type":"application/pdf","access_level":"open_access"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"acknowledgement":"Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron.","has_accepted_license":"1","oa":1,"file_date_updated":"2021-03-22T08:31:29Z","publication_status":"published","date_updated":"2025-06-12T06:35:22Z","volume":240,"arxiv":1,"month":"02","quality_controlled":"1","publication":"Archive for Rational Mechanics and Analysis","page":"383-417","article_type":"original","type":"journal_article","abstract":[{"text":"We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.","lang":"eng"}],"department":[{"_id":"RoSe"}],"ddc":["510"],"doi":"10.1007/s00205-021-01616-9","pmid":1,"oa_version":"Published Version","citation":{"chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>.","short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417.","mla":"Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240, Springer Nature, 2021, pp. 383–417, doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>.","ama":"Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. 2021;240:383-417. doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>","apa":"Leopold, N. K., Mitrouskas, D. J., &#38; Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>","ista":"Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.","ieee":"N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240. Springer Nature, pp. 383–417, 2021."},"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","last_name":"Leopold","full_name":"Leopold, Nikolai K","first_name":"Nikolai K"},{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert"}],"external_id":{"pmid":["33785964"],"isi":["000622226200001"],"arxiv":["2001.03993"]},"date_published":"2021-02-26T00:00:00Z","title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","status":"public"},{"publication":"Archive for Rational Mechanics and Analysis","month":"03","quality_controlled":"1","arxiv":1,"volume":236,"date_updated":"2025-04-14T07:27:00Z","publication_status":"published","file_date_updated":"2020-11-20T13:17:42Z","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions. Financial support by the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (Grant Agreement No. 694227) is gratefully acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 836146.","has_accepted_license":"1","status":"public","title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","date_published":"2020-03-09T00:00:00Z","external_id":{"arxiv":["1901.11363"],"isi":["000519415000001"]},"author":[{"first_name":"Andreas","full_name":"Deuchert, Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746"},{"first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Springer Nature","citation":{"ama":"Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271. doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>","ieee":"A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.","ista":"Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6), 1217–1271.","apa":"Deuchert, A., &#38; Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>","chicago":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>.","short":"A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236 (2020) 1217–1271.","mla":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>."},"oa_version":"Published Version","doi":"10.1007/s00205-020-01489-4","department":[{"_id":"RoSe"}],"ddc":["510"],"type":"journal_article","abstract":[{"lang":"eng","text":"We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Bose–Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution."}],"article_type":"original","page":"1217-1271","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_processing_charge":"Yes (via OA deal)","ec_funded":1,"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"issue":"6","scopus_import":"1","file":[{"file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","creator":"dernst","file_id":"8785","success":1,"date_updated":"2020-11-20T13:17:42Z","date_created":"2020-11-20T13:17:42Z","file_size":704633,"relation":"main_file","content_type":"application/pdf","checksum":"b645fb64bfe95bbc05b3eea374109a9c","access_level":"open_access"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"corr_author":"1","day":"09","_id":"7650","intvolume":"       236","language":[{"iso":"eng"}],"date_created":"2020-04-08T15:18:03Z","year":"2020","isi":1},{"intvolume":"       238","_id":"8130","language":[{"iso":"eng"}],"day":"01","corr_author":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"access_level":"open_access","content_type":"application/pdf","checksum":"cc67a79a67bef441625fcb1cd031db3d","relation":"main_file","file_size":942343,"date_created":"2020-12-02T08:50:38Z","date_updated":"2020-12-02T08:50:38Z","file_id":"8826","success":1,"creator":"dernst","file_name":"2020_ArchiveRatMech_Bossmann.pdf"}],"isi":1,"year":"2020","date_created":"2020-07-18T15:06:35Z","article_processing_charge":"Yes (via OA deal)","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"scopus_import":"1","issue":"11","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"ec_funded":1,"doi":"10.1007/s00205-020-01548-w","oa_version":"Published Version","citation":{"ama":"Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. 2020;238(11):541-606. doi:<a href=\"https://doi.org/10.1007/s00205-020-01548-w\">10.1007/s00205-020-01548-w</a>","ista":"Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.","apa":"Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01548-w\">https://doi.org/10.1007/s00205-020-01548-w</a>","ieee":"L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11. Springer Nature, pp. 541–606, 2020.","chicago":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01548-w\">https://doi.org/10.1007/s00205-020-01548-w</a>.","short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.","mla":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11, Springer Nature, 2020, pp. 541–606, doi:<a href=\"https://doi.org/10.1007/s00205-020-01548-w\">10.1007/s00205-020-01548-w</a>."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Springer Nature","author":[{"orcid":"0000-0002-6854-1343","last_name":"Bossmann","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","full_name":"Bossmann, Lea"}],"external_id":{"arxiv":["1907.04547"],"isi":["000550164400001"]},"date_published":"2020-11-01T00:00:00Z","title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","status":"public","page":"541-606","article_type":"original","abstract":[{"text":"We study the dynamics of a system of N interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to an interval of length of order ε. The interaction is non-negative and scaled in such a way that its scattering length is of order ε/N, while its range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein condensation. We prove that condensation is preserved by the N-body dynamics, where the time-evolved condensate wave function is the solution of a two-dimensional non-linear equation. The strength of the non-linearity depends on the scaling parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the scattering length of the interaction. In both cases, the coupling parameter depends on the confining potential.","lang":"eng"}],"type":"journal_article","department":[{"_id":"RoSe"}],"ddc":["510"],"date_updated":"2025-04-14T07:44:05Z","volume":238,"arxiv":1,"quality_controlled":"1","month":"11","publication":"Archive for Rational Mechanics and Analysis","has_accepted_license":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo and Nikolai Leopold are gratefully acknowledged. This work was supported by the German Research Foundation within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems” and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","oa":1,"file_date_updated":"2020-12-02T08:50:38Z","publication_status":"published"},{"doi":"10.1007/s00205-019-01486-2","oa_version":"Published Version","citation":{"short":"J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236 (2020) 967–1087.","mla":"Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:<a href=\"https://doi.org/10.1007/s00205-019-01486-2\">10.1007/s00205-019-01486-2</a>.","chicago":"Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-019-01486-2\">https://doi.org/10.1007/s00205-019-01486-2</a>.","apa":"Fischer, J. L., &#38; Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-019-01486-2\">https://doi.org/10.1007/s00205-019-01486-2</a>","ista":"Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. Archive for Rational Mechanics and Analysis. 236, 967–1087.","ieee":"J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236. Springer Nature, pp. 967–1087, 2020.","ama":"Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236:967-1087. doi:<a href=\"https://doi.org/10.1007/s00205-019-01486-2\">10.1007/s00205-019-01486-2</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","author":[{"full_name":"Fischer, Julian L","first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X"},{"orcid":"0000-0001-7252-8072","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","full_name":"Hensel, Sebastian","first_name":"Sebastian"}],"external_id":{"isi":["000511060200001"]},"date_published":"2020-05-01T00:00:00Z","title":"Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension","status":"public","page":"967-1087","article_type":"original","type":"journal_article","abstract":[{"lang":"eng","text":"In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our main result is a weak–strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier–Stokes equation: as long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities, the concept of varifold solutions—whose global in time existence has been shown by Abels (Interfaces Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy."}],"ddc":["530","532"],"department":[{"_id":"JuFi"}],"date_updated":"2026-04-08T07:01:01Z","volume":236,"quality_controlled":"1","month":"05","publication":"Archive for Rational Mechanics and Analysis","has_accepted_license":"1","oa":1,"file_date_updated":"2020-11-20T09:14:22Z","publication_status":"published","_id":"7489","intvolume":"       236","language":[{"iso":"eng"}],"day":"01","corr_author":"1","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"10007"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_size":1897571,"date_created":"2020-11-20T09:14:22Z","relation":"main_file","content_type":"application/pdf","checksum":"f107e21b58f5930876f47144be37cf6c","access_level":"open_access","file_name":"2020_ArchRatMechAn_Fischer.pdf","success":1,"creator":"dernst","file_id":"8779","date_updated":"2020-11-20T09:14:22Z"}],"isi":1,"year":"2020","date_created":"2020-02-16T23:00:50Z","article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"scopus_import":"1","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"ec_funded":1},{"type":"journal_article","abstract":[{"text":"The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: a sample of the random material is chosen—the representative volume—and its effective properties are computed by the cell formula. Intuitively, for a fixed sample size it should be possible to increase the accuracy of the method by choosing a material sample which captures the statistical properties of the material particularly well; for example, for a composite material consisting of two constituents, one would select a representative volume in which the volume fraction of the constituents matches closely with their volume fraction in the overall material. Inspired by similar attempts in materials science, Le Bris, Legoll and Minvielle have designed a selection approach for representative volumes which performs remarkably well in numerical examples of linear materials with moderate contrast. In the present work, we provide a rigorous analysis of this selection approach for representative volumes in the context of stochastic homogenization of linear elliptic equations. In particular, we prove that the method essentially never performs worse than a random selection of the material sample and may perform much better if the selection criterion for the material samples is chosen suitably.","lang":"eng"}],"ddc":["500"],"department":[{"_id":"JuFi"}],"page":"635–726","article_type":"original","status":"public","external_id":{"isi":["000482386000006"],"arxiv":["1807.00834"]},"date_published":"2019-11-01T00:00:00Z","title":"The choice of representative volumes in the approximation of effective properties of random materials","publisher":"Springer","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Fischer, Julian L. “The Choice of Representative Volumes in the Approximation of Effective Properties of Random Materials.” <i>Archive for Rational Mechanics and Analysis</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00205-019-01400-w\">https://doi.org/10.1007/s00205-019-01400-w</a>.","short":"J.L. Fischer, Archive for Rational Mechanics and Analysis 234 (2019) 635–726.","mla":"Fischer, Julian L. “The Choice of Representative Volumes in the Approximation of Effective Properties of Random Materials.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 234, no. 2, Springer, 2019, pp. 635–726, doi:<a href=\"https://doi.org/10.1007/s00205-019-01400-w\">10.1007/s00205-019-01400-w</a>.","ama":"Fischer JL. The choice of representative volumes in the approximation of effective properties of random materials. <i>Archive for Rational Mechanics and Analysis</i>. 2019;234(2):635–726. doi:<a href=\"https://doi.org/10.1007/s00205-019-01400-w\">10.1007/s00205-019-01400-w</a>","ieee":"J. L. Fischer, “The choice of representative volumes in the approximation of effective properties of random materials,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 234, no. 2. Springer, pp. 635–726, 2019.","ista":"Fischer JL. 2019. The choice of representative volumes in the approximation of effective properties of random materials. Archive for Rational Mechanics and Analysis. 234(2), 635–726.","apa":"Fischer, J. L. (2019). The choice of representative volumes in the approximation of effective properties of random materials. <i>Archive for Rational Mechanics and Analysis</i>. Springer. <a href=\"https://doi.org/10.1007/s00205-019-01400-w\">https://doi.org/10.1007/s00205-019-01400-w</a>"},"author":[{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L"}],"doi":"10.1007/s00205-019-01400-w","oa_version":"Published Version","publication_status":"published","oa":1,"file_date_updated":"2020-07-14T12:47:34Z","has_accepted_license":"1","publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"month":"11","quality_controlled":"1","volume":234,"date_updated":"2025-04-15T06:53:15Z","year":"2019","date_created":"2019-07-07T21:59:23Z","isi":1,"corr_author":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_name":"Springer_2019_Fischer.pdf","file_id":"6626","creator":"kschuh","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-08T15:56:47Z","file_size":1377659,"relation":"main_file","access_level":"open_access","checksum":"4cff75fa6addb0770991ad9c474ab404","content_type":"application/pdf"}],"_id":"6617","language":[{"iso":"eng"}],"intvolume":"       234","day":"01","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"scopus_import":"1","issue":"2","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_processing_charge":"Yes (via OA deal)"},{"oa":1,"publication_status":"published","arxiv":1,"quality_controlled":"1","month":"09","publication":"Archive for Rational Mechanics and Analysis","date_updated":"2025-04-15T08:26:15Z","volume":229,"type":"journal_article","abstract":[{"lang":"eng","text":"The Bogoliubov free energy functional is analysed. The functional serves as a model of a translation-invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove the existence of a phase transition in this model and provide its phase diagram."}],"department":[{"_id":"RoSe"}],"page":"1037-1090","external_id":{"arxiv":["1511.05935"],"isi":["000435367300003"]},"date_published":"2018-09-01T00:00:00Z","title":"The Bogoliubov free energy functional I: Existence of minimizers and phase diagram","status":"public","doi":"10.1007/s00205-018-1232-6","oa_version":"Preprint","citation":{"ama":"Napiórkowski MM, Reuvers R, Solovej JP. The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. <i>Archive for Rational Mechanics and Analysis</i>. 2018;229(3):1037-1090. doi:<a href=\"https://doi.org/10.1007/s00205-018-1232-6\">10.1007/s00205-018-1232-6</a>","apa":"Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. P. (2018). The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-018-1232-6\">https://doi.org/10.1007/s00205-018-1232-6</a>","ista":"Napiórkowski MM, Reuvers R, Solovej JP. 2018. The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. Archive for Rational Mechanics and Analysis. 229(3), 1037–1090.","ieee":"M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy functional I: Existence of minimizers and phase diagram,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 229, no. 3. Springer Nature, pp. 1037–1090, 2018.","chicago":"Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00205-018-1232-6\">https://doi.org/10.1007/s00205-018-1232-6</a>.","short":"M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics and Analysis 229 (2018) 1037–1090.","mla":"Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:<a href=\"https://doi.org/10.1007/s00205-018-1232-6\">10.1007/s00205-018-1232-6</a>."},"publisher":"Springer Nature","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","first_name":"Marcin M","full_name":"Napiórkowski, Marcin M"},{"full_name":"Reuvers, Robin","first_name":"Robin","last_name":"Reuvers"},{"first_name":"Jan Philip","full_name":"Solovej, Jan Philip","last_name":"Solovej"}],"scopus_import":"1","issue":"3","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"project":[{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"article_processing_charge":"No","year":"2018","date_created":"2019-02-14T13:40:53Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.05935"}],"isi":1,"intvolume":"       229","_id":"6002","language":[{"iso":"eng"}],"day":"01"},{"type":"journal_article","abstract":[{"text":"We consider the cubic–quintic nonlinear Schrödinger equation: (mathematical formular)\r\nIn the first part of the paper, we analyze the one-parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass/energy curve. Additionally, we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one-parameter family of inequalities of Gagliardo–Nirenberg type. Building on this work, in the latter part of the paper we prove that scattering holds for solutions belonging to the region R of the mass/energy plane where the virial is positive. We show that this region is partially bounded by solitons also by rescalings of solitons (which are not soliton solutions in their own right). The discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial-based methodology.","lang":"eng"}],"OA_type":"green","page":"469-548","article_type":"original","status":"public","external_id":{"arxiv":["1409.6734"]},"date_published":"2017-07-01T00:00:00Z","title":"Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3","publisher":"Springer Nature","citation":{"mla":"Killip, Rowan, et al. “Solitons and Scattering for the Cubic-Quintic Nonlinear Schrödinger Equation on R^3.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 225, Springer Nature, 2017, pp. 469–548, doi:<a href=\"https://doi.org/10.1007/s00205-017-1109-0\">10.1007/s00205-017-1109-0</a>.","short":"R. Killip, T. Oh, O. Pocovnicu, M. Vişan, Archive for Rational Mechanics and Analysis 225 (2017) 469–548.","chicago":"Killip, Rowan, Tadahiro Oh, Oana Pocovnicu, and Monica Vişan. “Solitons and Scattering for the Cubic-Quintic Nonlinear Schrödinger Equation on R^3.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2017. <a href=\"https://doi.org/10.1007/s00205-017-1109-0\">https://doi.org/10.1007/s00205-017-1109-0</a>.","ieee":"R. Killip, T. Oh, O. Pocovnicu, and M. Vişan, “Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 225. Springer Nature, pp. 469–548, 2017.","apa":"Killip, R., Oh, T., Pocovnicu, O., &#38; Vişan, M. (2017). Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-017-1109-0\">https://doi.org/10.1007/s00205-017-1109-0</a>","ista":"Killip R, Oh T, Pocovnicu O, Vişan M. 2017. Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3. Archive for Rational Mechanics and Analysis. 225, 469–548.","ama":"Killip R, Oh T, Pocovnicu O, Vişan M. Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3. <i>Archive for Rational Mechanics and Analysis</i>. 2017;225:469-548. doi:<a href=\"https://doi.org/10.1007/s00205-017-1109-0\">10.1007/s00205-017-1109-0</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Oh, Tadahiro","first_name":"Tadahiro","last_name":"Oh"},{"full_name":"Pocovnicu, Oana","first_name":"Oana","last_name":"Pocovnicu"},{"first_name":"Monica","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"doi":"10.1007/s00205-017-1109-0","oa_version":"Preprint","OA_place":"repository","publication_status":"published","oa":1,"publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"month":"07","quality_controlled":"1","volume":225,"date_updated":"2026-06-30T10:52:12Z","date_created":"2026-06-19T08:21:38Z","year":"2017","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1409.6734","open_access":"1"}],"_id":"22071","language":[{"iso":"eng"}],"intvolume":"       225","day":"01","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"scopus_import":"1","extern":"1","article_processing_charge":"No"},{"type":"journal_article","abstract":[{"lang":"eng","text":"In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction–diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions."}],"OA_type":"green","page":"553 - 587","article_type":"original","date_published":"2015-10-01T00:00:00Z","title":"Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems","status":"public","doi":"10.1007/s00205-015-0866-x","OA_place":"repository","oa_version":"Preprint","publisher":"Springer Nature","citation":{"short":"J.L. Fischer, Archive for Rational Mechanics and Analysis 218 (2015) 553–587.","mla":"Fischer, Julian L. “Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 218, Springer Nature, 2015, pp. 553–87, doi:<a href=\"https://doi.org/10.1007/s00205-015-0866-x\">10.1007/s00205-015-0866-x</a>.","chicago":"Fischer, Julian L. “Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/s00205-015-0866-x\">https://doi.org/10.1007/s00205-015-0866-x</a>.","ieee":"J. L. Fischer, “Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 218. Springer Nature, pp. 553–587, 2015.","apa":"Fischer, J. L. (2015). Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-015-0866-x\">https://doi.org/10.1007/s00205-015-0866-x</a>","ista":"Fischer JL. 2015. Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems. Archive for Rational Mechanics and Analysis. 218, 553–587.","ama":"Fischer JL. Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems. <i>Archive for Rational Mechanics and Analysis</i>. 2015;218:553-587. doi:<a href=\"https://doi.org/10.1007/s00205-015-0866-x\">10.1007/s00205-015-0866-x</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Fischer, Julian L","first_name":"Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer"}],"oa":1,"publication_status":"published","publist_id":"5955","acknowledgement":"This research was supported by the Lithuanian-Swiss cooperation program under the project agreement No. CH-SMM-01/0.","month":"10","quality_controlled":"1","publication":"Archive for Rational Mechanics and Analysis","date_updated":"2026-06-02T09:04:47Z","volume":218,"year":"2015","date_created":"2018-12-11T11:51:20Z","main_file_link":[{"url":"http://www.j-fischer.eu/pdf/reactdiffexist.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"_id":"1316","intvolume":"       218","day":"01","scopus_import":"1","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"article_processing_charge":"No","extern":"1"}]