[{"type":"journal_article","date_published":"2023-08-01T00:00:00Z","external_id":{"arxiv":["2106.13185"],"isi":["001024369000001"]},"publisher":"Springer Nature","status":"public","isi":1,"month":"08","ddc":["510"],"language":[{"iso":"eng"}],"quality_controlled":"1","day":"01","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"}],"issue":"4","volume":247,"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Niels P","last_name":"Benedikter","orcid":"0000-0002-1071-6091","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","full_name":"Benedikter, Niels P"},{"full_name":"Porta, Marcello","first_name":"Marcello","last_name":"Porta"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"date_updated":"2023-12-13T11:31:14Z","ec_funded":1,"publication":"Archive for Rational Mechanics and Analysis","department":[{"_id":"RoSe"}],"intvolume":"       247","arxiv":1,"article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","file_date_updated":"2023-11-14T13:12:12Z","publication_status":"published","title":"Correlation energy of a weakly interacting Fermi gas with large interaction potential","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"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_type":"original","scopus_import":"1","doi":"10.1007/s00205-023-01893-6","date_created":"2023-07-16T22:01:08Z","file":[{"success":1,"access_level":"open_access","file_name":"2023_ArchiveRationalMechAnalysis_Benedikter.pdf","file_size":851626,"relation":"main_file","date_updated":"2023-11-14T13:12:12Z","date_created":"2023-11-14T13:12:12Z","content_type":"application/pdf","file_id":"14535","creator":"dernst","checksum":"2b45828d854a253b14bf7aa196ec55e9"}],"_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."}],"citation":{"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.","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>","short":"N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023).","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>.","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>","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>."},"year":"2023","article_number":"65"},{"date_updated":"2024-01-30T12:10:10Z","ec_funded":1,"publication":"Archive for Rational Mechanics and Analysis","department":[{"_id":"JuFi"}],"intvolume":"       247","arxiv":1,"volume":247,"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Cornalba, Federico","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149","last_name":"Cornalba","first_name":"Federico"},{"first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"}],"date_created":"2021-12-16T12:16:03Z","file":[{"access_level":"open_access","success":1,"file_name":"2023_ArchiveRationalMech_Cornalba.pdf","relation":"main_file","file_size":1851185,"date_updated":"2024-01-30T12:09:34Z","date_created":"2024-01-30T12:09:34Z","file_id":"14904","creator":"dernst","content_type":"application/pdf","checksum":"4529eeff170b6745a461d397ee611b5a"}],"_id":"10551","abstract":[{"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.","lang":"eng"}],"citation":{"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>","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.","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>.","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>","short":"F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023).","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>."},"article_number":"76","year":"2023","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2024-01-30T12:09:34Z","publication_status":"published","title":"The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles","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_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00205-023-01903-7","status":"public","isi":1,"month":"08","ddc":["510"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2023-08-04T00:00:00Z","external_id":{"arxiv":["2109.06500"],"isi":["001043086800001"]},"publisher":"Springer Nature","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","issue":"5","quality_controlled":"1","day":"04"},{"file":[{"creator":"alisjak","file_id":"10544","content_type":"application/pdf","checksum":"672e9c21b20f1a50854b7c821edbb92f","file_name":"2021_Springer_Feliciangeli.pdf","access_level":"open_access","success":1,"file_size":990529,"relation":"main_file","date_updated":"2021-12-14T08:35:42Z","date_created":"2021-12-14T08:35:42Z"}],"date_created":"2021-11-07T23:01:26Z","_id":"10224","citation":{"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>","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>.","short":"D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis 242 (2021) 1835–1906.","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>.","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.","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>"},"year":"2021","abstract":[{"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.","lang":"eng"}],"title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics","publication_status":"published","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2021-12-14T08:35:42Z","scopus_import":"1","doi":"10.1007/s00205-021-01715-7","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"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).","article_type":"original","department":[{"_id":"RoSe"}],"ec_funded":1,"date_updated":"2023-08-14T10:32:19Z","publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"intvolume":"       242","volume":242,"oa":1,"related_material":{"record":[{"id":"9787","status":"public","relation":"earlier_version"}]},"author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","first_name":"Dario"},{"first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"3","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"}],"quality_controlled":"1","page":"1835–1906","day":"25","isi":1,"month":"10","status":"public","ddc":["530"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2021-10-25T00:00:00Z","external_id":{"arxiv":["2101.12566"],"isi":["000710850600001"]},"publisher":"Springer Nature"},{"issue":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","page":"343-452","day":"30","quality_controlled":"1","ddc":["530"],"language":[{"iso":"eng"}],"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"isi":1,"month":"06","status":"public","publisher":"Springer Nature","type":"journal_article","date_published":"2021-06-30T00:00:00Z","external_id":{"arxiv":["1908.02273"],"isi":["000668431200001"]},"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>.","short":"J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 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>","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>.","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.","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.","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>"},"year":"2021","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."}],"file":[{"file_name":"2021_ArchRatMechAnalysis_Fischer.pdf","access_level":"open_access","success":1,"date_updated":"2021-12-16T14:58:08Z","relation":"main_file","file_size":1640121,"date_created":"2021-12-16T14:58:08Z","creator":"cchlebak","file_id":"10558","content_type":"application/pdf","checksum":"cc830b739aed83ca2e32c4e0ce266a4c"}],"date_created":"2021-12-16T12:12:33Z","_id":"10549","scopus_import":"1","doi":"10.1007/s00205-021-01686-9","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"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.","article_type":"original","publication_status":"published","title":"Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2021-12-16T14:58:08Z","arxiv":1,"intvolume":"       242","department":[{"_id":"JuFi"}],"date_updated":"2023-08-17T06:23:21Z","publication":"Archive for Rational Mechanics and Analysis","author":[{"first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L"},{"first_name":"Stefan","last_name":"Neukamm","full_name":"Neukamm, Stefan"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","volume":242,"oa":1},{"title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","publication_status":"published","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","file_date_updated":"2020-11-20T13:17:42Z","scopus_import":"1","doi":"10.1007/s00205-020-01489-4","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.","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"article_type":"original","file":[{"content_type":"application/pdf","file_id":"8785","creator":"dernst","checksum":"b645fb64bfe95bbc05b3eea374109a9c","file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","success":1,"access_level":"open_access","file_size":704633,"date_updated":"2020-11-20T13:17:42Z","date_created":"2020-11-20T13:17:42Z","relation":"main_file"}],"date_created":"2020-04-08T15:18:03Z","_id":"7650","citation":{"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>.","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.","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>"},"year":"2020","abstract":[{"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.","lang":"eng"}],"volume":236,"oa":1,"author":[{"first_name":"Andreas","last_name":"Deuchert","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","full_name":"Deuchert, Andreas"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"RoSe"}],"date_updated":"2023-09-05T14:18:49Z","ec_funded":1,"publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"intvolume":"       236","quality_controlled":"1","page":"1217-1271","day":"09","issue":"6","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"type":"journal_article","external_id":{"isi":["000519415000001"],"arxiv":["1901.11363"]},"date_published":"2020-03-09T00:00:00Z","publisher":"Springer Nature","isi":1,"month":"03","status":"public","ddc":["510"],"language":[{"iso":"eng"}]},{"quality_controlled":"1","day":"01","page":"541-606","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"issue":"11","type":"journal_article","date_published":"2020-11-01T00:00:00Z","external_id":{"isi":["000550164400001"],"arxiv":["1907.04547"]},"publisher":"Springer Nature","status":"public","isi":1,"month":"11","ddc":["510"],"language":[{"iso":"eng"}],"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2020-12-02T08:50:38Z","publication_status":"published","title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","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.","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00205-020-01548-w","date_created":"2020-07-18T15:06:35Z","file":[{"success":1,"access_level":"open_access","file_name":"2020_ArchiveRatMech_Bossmann.pdf","date_created":"2020-12-02T08:50:38Z","date_updated":"2020-12-02T08:50:38Z","file_size":942343,"relation":"main_file","file_id":"8826","creator":"dernst","content_type":"application/pdf","checksum":"cc67a79a67bef441625fcb1cd031db3d"}],"_id":"8130","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"}],"citation":{"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.","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.","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>","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>.","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>","short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.","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>."},"year":"2020","volume":238,"oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","last_name":"Bossmann","first_name":"Lea"}],"date_updated":"2023-09-05T14:19:06Z","ec_funded":1,"publication":"Archive for Rational Mechanics and Analysis","department":[{"_id":"RoSe"}],"intvolume":"       238","arxiv":1},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00205-019-01368-7"}],"doi":"10.1007/s00205-019-01368-7","article_type":"original","publication_identifier":{"issn":["0003-9527","1432-0673"]},"title":"Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem","publication_status":"published","oa_version":"Published Version","article_processing_charge":"No","year":"2019","citation":{"ista":"Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 233(2), 799–836.","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019.","ama":"Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. <i>Archive for Rational Mechanics and Analysis</i>. 2019;233(2):799-836. doi:<a href=\"https://doi.org/10.1007/s00205-019-01368-7\">10.1007/s00205-019-01368-7</a>","mla":"Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:<a href=\"https://doi.org/10.1007/s00205-019-01368-7\">10.1007/s00205-019-01368-7</a>.","chicago":"Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00205-019-01368-7\">https://doi.org/10.1007/s00205-019-01368-7</a>.","short":"M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis 233 (2019) 799–836.","apa":"Guardia, M., Kaloshin, V., &#38; Zhang, J. (2019). Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-019-01368-7\">https://doi.org/10.1007/s00205-019-01368-7</a>"},"abstract":[{"text":"For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0.","lang":"eng"}],"_id":"8418","date_created":"2020-09-17T10:41:51Z","author":[{"full_name":"Guardia, Marcel","last_name":"Guardia","first_name":"Marcel"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim"},{"last_name":"Zhang","first_name":"Jianlu","full_name":"Zhang, Jianlu"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"volume":233,"intvolume":"       233","publication":"Archive for Rational Mechanics and Analysis","date_updated":"2021-01-12T08:19:09Z","page":"799-836","day":"12","quality_controlled":"1","issue":"2","publisher":"Springer Nature","date_published":"2019-03-12T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"extern":"1","month":"03","status":"public"},{"department":[{"_id":"JuFi"}],"date_updated":"2023-08-28T12:31:21Z","publication":"Archive for Rational Mechanics and Analysis","arxiv":1,"intvolume":"       234","volume":234,"oa":1,"author":[{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2019-07-07T21:59:23Z","file":[{"date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-08T15:56:47Z","relation":"main_file","file_size":1377659,"access_level":"open_access","file_name":"Springer_2019_Fischer.pdf","checksum":"4cff75fa6addb0770991ad9c474ab404","content_type":"application/pdf","file_id":"6626","creator":"kschuh"}],"_id":"6617","citation":{"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>","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.","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.","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>.","short":"J.L. Fischer, Archive for Rational Mechanics and Analysis 234 (2019) 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>","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>."},"year":"2019","abstract":[{"lang":"eng","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."}],"publication_status":"published","title":"The choice of representative volumes in the approximation of effective properties of random materials","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","file_date_updated":"2020-07-14T12:47:34Z","scopus_import":"1","doi":"10.1007/s00205-019-01400-w","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"article_type":"original","isi":1,"month":"11","status":"public","ddc":["500"],"language":[{"iso":"eng"}],"type":"journal_article","external_id":{"isi":["000482386000006"],"arxiv":["1807.00834"]},"date_published":"2019-11-01T00:00:00Z","publisher":"Springer","issue":"2","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","page":"635–726","day":"01"},{"quality_controlled":"1","page":"1037-1090","day":"01","issue":"3","project":[{"call_identifier":"FWF","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"date_published":"2018-09-01T00:00:00Z","external_id":{"isi":["000435367300003"],"arxiv":["1511.05935"]},"type":"journal_article","publisher":"Springer Nature","month":"09","isi":1,"status":"public","language":[{"iso":"eng"}],"publication_status":"published","title":"The Bogoliubov free energy functional I: Existence of minimizers and phase diagram","oa_version":"Preprint","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.05935"}],"doi":"10.1007/s00205-018-1232-6","scopus_import":"1","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"_id":"6002","date_created":"2019-02-14T13:40:53Z","year":"2018","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>","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.","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.","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>.","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>.","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>","short":"M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics and Analysis 229 (2018) 1037–1090."},"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."}],"oa":1,"volume":229,"author":[{"full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","first_name":"Marcin M"},{"first_name":"Robin","last_name":"Reuvers","full_name":"Reuvers, Robin"},{"full_name":"Solovej, Jan Philip","first_name":"Jan Philip","last_name":"Solovej"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"RoSe"}],"publication":"Archive for Rational Mechanics and Analysis","date_updated":"2023-09-19T14:33:12Z","arxiv":1,"intvolume":"       229"}]