[{"date_updated":"2024-08-07T07:16:53Z","status":"public","day":"27","oa_version":"Preprint","publication_status":"published","abstract":[{"text":"Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born–Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.","lang":"eng"}],"ec_funded":1,"citation":{"ama":"Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. Intermolecular forces and correlations mediated by a phonon bath. <i>The Journal of Chemical Physics</i>. 2020;152(16). doi:<a href=\"https://doi.org/10.1063/1.5144759\">10.1063/1.5144759</a>","ista":"Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. 2020. Intermolecular forces and correlations mediated by a phonon bath. The Journal of Chemical Physics. 152(16), 164302.","apa":"Li, X., Yakaboylu, E., Bighin, G., Schmidt, R., Lemeshko, M., &#38; Deuchert, A. (2020). Intermolecular forces and correlations mediated by a phonon bath. <i>The Journal of Chemical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.5144759\">https://doi.org/10.1063/1.5144759</a>","mla":"Li, Xiang, et al. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” <i>The Journal of Chemical Physics</i>, vol. 152, no. 16, 164302, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/1.5144759\">10.1063/1.5144759</a>.","short":"X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, A. Deuchert, The Journal of Chemical Physics 152 (2020).","ieee":"X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, and A. Deuchert, “Intermolecular forces and correlations mediated by a phonon bath,” <i>The Journal of Chemical Physics</i>, vol. 152, no. 16. AIP Publishing, 2020.","chicago":"Li, Xiang, Enderalp Yakaboylu, Giacomo Bighin, Richard Schmidt, Mikhail Lemeshko, and Andreas Deuchert. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” <i>The Journal of Chemical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/1.5144759\">https://doi.org/10.1063/1.5144759</a>."},"arxiv":1,"project":[{"_id":"26031614-B435-11E9-9278-68D0E5697425","name":"Quantum rotations in the presence of a many-body environment","call_identifier":"FWF","grant_number":"P29902"},{"_id":"2688CF98-B435-11E9-9278-68D0E5697425","name":"Angulon: physics and applications of a new quasiparticle","grant_number":"801770","call_identifier":"H2020"},{"_id":"26986C82-B435-11E9-9278-68D0E5697425","name":"A path-integral approach to composite impurities","call_identifier":"FWF","grant_number":"M02641"},{"call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}],"issue":"16","main_file_link":[{"url":"https://arxiv.org/abs/1912.02658","open_access":"1"}],"publication":"The Journal of Chemical Physics","title":"Intermolecular forces and correlations mediated by a phonon bath","external_id":{"arxiv":["1912.02658"],"isi":["000530448300001"]},"related_material":{"record":[{"id":"8958","status":"public","relation":"dissertation_contains"}]},"doi":"10.1063/1.5144759","language":[{"iso":"eng"}],"year":"2020","publisher":"AIP Publishing","type":"journal_article","author":[{"id":"4B7E523C-F248-11E8-B48F-1D18A9856A87","last_name":"Li","first_name":"Xiang","full_name":"Li, Xiang"},{"orcid":"0000-0001-5973-0874","last_name":"Yakaboylu","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","first_name":"Enderalp","full_name":"Yakaboylu, Enderalp"},{"orcid":"0000-0001-8823-9777","last_name":"Bighin","id":"4CA96FD4-F248-11E8-B48F-1D18A9856A87","first_name":"Giacomo","full_name":"Bighin, Giacomo"},{"last_name":"Schmidt","first_name":"Richard","full_name":"Schmidt, Richard"},{"full_name":"Lemeshko, Mikhail","first_name":"Mikhail","last_name":"Lemeshko","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802"},{"first_name":"Andreas","full_name":"Deuchert, Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert"}],"_id":"8587","oa":1,"date_published":"2020-04-27T00:00:00Z","date_created":"2020-09-30T10:33:17Z","article_number":"164302","acknowledgement":"We are grateful to Areg Ghazaryan for valuable discussions. M.L. acknowledges support from the Austrian Science Fund (FWF) under Project No. P29902-N27 and from the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). G.B. acknowledges support from the Austrian Science Fund (FWF) under Project No. M2461-N27. A.D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the European Research Council (ERC) Grant Agreement No. 694227 and under the Marie Sklodowska-Curie Grant Agreement No. 836146. R.S. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2111 – 390814868.","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":"       152","keyword":["Physical and Theoretical Chemistry","General Physics and Astronomy"],"month":"04","publication_identifier":{"eissn":["1089-7690"],"issn":["0021-9606"]},"quality_controlled":"1","isi":1,"volume":152,"article_type":"original"},{"date_updated":"2023-09-07T13:43:51Z","status":"public","abstract":[{"lang":"eng","text":"We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fröhlich polaron model."}],"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","page":"4003-4025","publication_status":"published","oa_version":"Published Version","citation":{"chicago":"Mysliwy, Krzysztof, and Robert Seiringer. “Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit.” <i>Annales Henri Poincare</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00023-020-00969-3\">https://doi.org/10.1007/s00023-020-00969-3</a>.","ieee":"K. Mysliwy and R. Seiringer, “Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit,” <i>Annales Henri Poincare</i>, vol. 21, no. 12. Springer Nature, pp. 4003–4025, 2020.","apa":"Mysliwy, K., &#38; Seiringer, R. (2020). Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-020-00969-3\">https://doi.org/10.1007/s00023-020-00969-3</a>","short":"K. Mysliwy, R. Seiringer, Annales Henri Poincare 21 (2020) 4003–4025.","mla":"Mysliwy, Krzysztof, and Robert Seiringer. “Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit.” <i>Annales Henri Poincare</i>, vol. 21, no. 12, Springer Nature, 2020, pp. 4003–25, doi:<a href=\"https://doi.org/10.1007/s00023-020-00969-3\">10.1007/s00023-020-00969-3</a>.","ista":"Mysliwy K, Seiringer R. 2020. Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. Annales Henri Poincare. 21(12), 4003–4025.","ama":"Mysliwy K, Seiringer R. Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. <i>Annales Henri Poincare</i>. 2020;21(12):4003-4025. doi:<a href=\"https://doi.org/10.1007/s00023-020-00969-3\">10.1007/s00023-020-00969-3</a>"},"arxiv":1,"project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","scopus_import":"1","issue":"12","title":"Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit","file":[{"date_updated":"2020-10-27T12:49:04Z","success":1,"checksum":"c12c9c1e6f08def245e42f3cb1d83827","file_id":"8711","date_created":"2020-10-27T12:49:04Z","file_size":469831,"file_name":"2020_Annales_Mysliwy.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"cziletti"}],"external_id":{"isi":["000578111800002"],"arxiv":["2003.12371"]},"related_material":{"record":[{"status":"public","id":"11473","relation":"dissertation_contains"}]},"publication":"Annales Henri Poincare","year":"2020","publisher":"Springer Nature","doi":"10.1007/s00023-020-00969-3","language":[{"iso":"eng"}],"type":"journal_article","_id":"8705","oa":1,"author":[{"full_name":"Mysliwy, Krzysztof","first_name":"Krzysztof","last_name":"Mysliwy","id":"316457FC-F248-11E8-B48F-1D18A9856A87"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert"}],"date_published":"2020-12-01T00:00:00Z","department":[{"_id":"RoSe"}],"acknowledgement":"Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie Grant agreement No. 665386 (K.M.) is gratefully acknowledged. Funding Open access funding provided by Institute of Science and Technology (IST Austria)","date_created":"2020-10-25T23:01:19Z","intvolume":"        21","file_date_updated":"2020-10-27T12:49:04Z","ddc":["530"],"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["1424-0637"]},"quality_controlled":"1","month":"12","article_type":"original","volume":21,"isi":1},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1912.07890"}],"title":"Quantum impurity model for anyons","external_id":{"isi":["000582563300001"],"arxiv":["1912.07890"]},"publication":"Physical Review B","citation":{"chicago":"Yakaboylu, Enderalp, Areg Ghazaryan, D. Lundholm, N. Rougerie, Mikhail Lemeshko, and Robert Seiringer. “Quantum Impurity Model for Anyons.” <i>Physical Review B</i>. American Physical Society, 2020. <a href=\"https://doi.org/10.1103/physrevb.102.144109\">https://doi.org/10.1103/physrevb.102.144109</a>.","ieee":"E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, and R. Seiringer, “Quantum impurity model for anyons,” <i>Physical Review B</i>, vol. 102, no. 14. American Physical Society, 2020.","short":"E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, R. Seiringer, Physical Review B 102 (2020).","ista":"Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R. 2020. Quantum impurity model for anyons. Physical Review B. 102(14), 144109.","mla":"Yakaboylu, Enderalp, et al. “Quantum Impurity Model for Anyons.” <i>Physical Review B</i>, vol. 102, no. 14, 144109, American Physical Society, 2020, doi:<a href=\"https://doi.org/10.1103/physrevb.102.144109\">10.1103/physrevb.102.144109</a>.","apa":"Yakaboylu, E., Ghazaryan, A., Lundholm, D., Rougerie, N., Lemeshko, M., &#38; Seiringer, R. (2020). Quantum impurity model for anyons. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevb.102.144109\">https://doi.org/10.1103/physrevb.102.144109</a>","ama":"Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R. Quantum impurity model for anyons. <i>Physical Review B</i>. 2020;102(14). doi:<a href=\"https://doi.org/10.1103/physrevb.102.144109\">10.1103/physrevb.102.144109</a>"},"arxiv":1,"project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"_id":"2688CF98-B435-11E9-9278-68D0E5697425","name":"Angulon: physics and applications of a new quasiparticle","grant_number":"801770","call_identifier":"H2020"}],"scopus_import":"1","issue":"14","abstract":[{"lang":"eng","text":"One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have not yet been unambiguously detected in experiment. Here we introduce a simple quantum impurity model, where bosonic or fermionic impurities turn into anyons as a consequence of their interaction with the surrounding many-particle bath. A cloud of phonons dresses each impurity in such a way that it effectively attaches fluxes or vortices to it and thereby converts it into an Abelian anyon. The corresponding quantum impurity model, first, provides a different approach to the numerical solution of the many-anyon problem, along with a concrete perspective of anyons as emergent quasiparticles built from composite bosons or fermions. More importantly, the model paves the way toward realizing anyons using impurities in crystal lattices as well as ultracold gases. In particular, we consider two heavy electrons interacting with a two-dimensional lattice crystal in a magnetic field, and show that when the impurity-bath system is rotated at the cyclotron frequency, impurities behave as anyons as a consequence of the angular momentum exchange between the impurities and the bath. A possible experimental realization is proposed by identifying the statistics parameter in terms of the mean-square distance of the impurities and the magnetization of the impurity-bath system, both of which are accessible to experiment. Another proposed application is impurities immersed in a two-dimensional weakly interacting Bose gas."}],"ec_funded":1,"day":"01","publication_status":"published","oa_version":"Preprint","date_updated":"2023-09-05T12:12:30Z","status":"public","publication_identifier":{"issn":["2469-9950"],"eissn":["2469-9969"]},"quality_controlled":"1","month":"10","volume":102,"article_type":"original","isi":1,"acknowledgement":"We are grateful to M. Correggi, A. Deuchert, and P. Schmelcher for valuable discussions. We also thank the anonymous referees for helping to clarify a few important points in the experimental realization. A.G. acknowledges support by the European Unions Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement\r\nNo 754411. D.L. acknowledges financial support from the Goran Gustafsson Foundation (grant no. 1804) and LMU Munich. R.S., M.L., and N.R. gratefully acknowledge financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 694227, No 801770, and No 758620, respectively).","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"date_created":"2020-11-18T07:34:17Z","article_number":"144109","intvolume":"       102","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","_id":"8769","oa":1,"author":[{"first_name":"Enderalp","full_name":"Yakaboylu, Enderalp","orcid":"0000-0001-5973-0874","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","last_name":"Yakaboylu"},{"orcid":"0000-0001-9666-3543","id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87","last_name":"Ghazaryan","full_name":"Ghazaryan, Areg","first_name":"Areg"},{"full_name":"Lundholm, D.","first_name":"D.","last_name":"Lundholm"},{"last_name":"Rougerie","full_name":"Rougerie, N.","first_name":"N."},{"first_name":"Mikhail","full_name":"Lemeshko, Mikhail","last_name":"Lemeshko","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802"},{"first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"date_published":"2020-10-01T00:00:00Z","year":"2020","publisher":"American Physical Society","doi":"10.1103/physrevb.102.144109","language":[{"iso":"eng"}],"type":"journal_article"},{"has_accepted_license":"1","scopus_import":"1","project":[{"call_identifier":"FWF","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund"},{"call_identifier":"FWF","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"}],"citation":{"ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp. 2097–2150, 2020.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>","mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>.","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150."},"arxiv":1,"external_id":{"isi":["000527910700019"],"arxiv":["1809.01902"]},"title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":853289,"file_name":"2019_CommMathPhysics_Benedikter.pdf","date_updated":"2020-07-14T12:47:35Z","file_id":"6668","date_created":"2019-07-24T07:19:10Z","checksum":"f9dd6dd615a698f1d3636c4a092fed23"}],"publication":"Communications in Mathematical Physics","status":"public","date_updated":"2023-08-17T13:51:50Z","ec_funded":1,"abstract":[{"lang":"eng","text":"While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.\r\n"}],"oa_version":"Published Version","publication_status":"published","page":"2097–2150","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","intvolume":"       374","ddc":["530"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","file_date_updated":"2020-07-14T12:47:35Z","department":[{"_id":"RoSe"}],"date_created":"2019-07-18T13:30:04Z","volume":374,"article_type":"original","isi":1,"quality_controlled":"1","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"month":"03","type":"journal_article","publisher":"Springer Nature","year":"2020","language":[{"iso":"eng"}],"doi":"10.1007/s00220-019-03505-5","date_published":"2020-03-01T00:00:00Z","oa":1,"_id":"6649","author":[{"id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter","orcid":"0000-0002-1071-6091","first_name":"Niels P","full_name":"Benedikter, Niels P"},{"last_name":"Nam","full_name":"Nam, Phan Thành","first_name":"Phan Thành"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}]},{"abstract":[{"lang":"eng","text":"We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential."}],"ec_funded":1,"day":"01","oa_version":"Preprint","page":"1311-1395","publication_status":"published","date_updated":"2024-02-22T13:33:02Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1812.03086"}],"title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","external_id":{"isi":["000536053300012"],"arxiv":["1812.03086"]},"publication":"Communications in Mathematical Physics","citation":{"short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395.","mla":"Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer, 2020, pp. 1311–95, doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. 376, 1311–1395.","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. 2020;376:1311-1395. doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>.","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer, pp. 1311–1395, 2020."},"arxiv":1,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"}],"scopus_import":"1","_id":"6906","oa":1,"author":[{"first_name":"Chiara","full_name":"Boccato, Chiara","last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Christian","full_name":"Brennecke, Christian","last_name":"Brennecke"},{"last_name":"Cenatiempo","first_name":"Serena","full_name":"Cenatiempo, Serena"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"}],"date_published":"2020-06-01T00:00:00Z","year":"2020","publisher":"Springer","doi":"10.1007/s00220-019-03555-9","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"quality_controlled":"1","month":"06","volume":376,"article_type":"original","isi":1,"acknowledgement":"We would like to thank P. T. Nam and R. Seiringer for several useful discussions and\r\nfor suggesting us to use the localization techniques from [9]. C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges support from the NCCR SwissMAP and from the Swiss National Foundation of Science (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties of Bose–Einstein condensates”.","department":[{"_id":"RoSe"}],"date_created":"2019-09-24T17:30:59Z","intvolume":"       376","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No"},{"abstract":[{"lang":"eng","text":"We consider the Fröhlich model of a polaron, and show that its effective mass diverges in thestrong coupling limit."}],"ec_funded":1,"day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","oa_version":"Published Version","page":"23-33","status":"public","date_updated":"2023-09-05T14:57:29Z","title":"Divergence of the effective mass of a polaron in the strong coupling limit","file":[{"date_created":"2020-11-19T11:13:55Z","file_id":"8774","checksum":"1e67bee6728592f7bdcea2ad2d9366dc","date_updated":"2020-11-19T11:13:55Z","success":1,"file_name":"2020_JourStatPhysics_Lieb.pdf","file_size":279749,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"dernst"}],"external_id":{"isi":["000556199700003"]},"publication":"Journal of Statistical Physics","has_accepted_license":"1","scopus_import":"1","citation":{"chicago":"Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-019-02322-3\">https://doi.org/10.1007/s10955-019-02322-3</a>.","ieee":"E. H. Lieb and R. Seiringer, “Divergence of the effective mass of a polaron in the strong coupling limit,” <i>Journal of Statistical Physics</i>, vol. 180. Springer Nature, pp. 23–33, 2020.","apa":"Lieb, E. H., &#38; Seiringer, R. (2020). Divergence of the effective mass of a polaron in the strong coupling limit. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-019-02322-3\">https://doi.org/10.1007/s10955-019-02322-3</a>","short":"E.H. Lieb, R. Seiringer, Journal of Statistical Physics 180 (2020) 23–33.","mla":"Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” <i>Journal of Statistical Physics</i>, vol. 180, Springer Nature, 2020, pp. 23–33, doi:<a href=\"https://doi.org/10.1007/s10955-019-02322-3\">10.1007/s10955-019-02322-3</a>.","ista":"Lieb EH, Seiringer R. 2020. Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. 180, 23–33.","ama":"Lieb EH, Seiringer R. Divergence of the effective mass of a polaron in the strong coupling limit. <i>Journal of Statistical Physics</i>. 2020;180:23-33. doi:<a href=\"https://doi.org/10.1007/s10955-019-02322-3\">10.1007/s10955-019-02322-3</a>"},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"date_published":"2020-09-01T00:00:00Z","_id":"7235","oa":1,"author":[{"full_name":"Lieb, Elliott H.","first_name":"Elliott H.","last_name":"Lieb"},{"first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"type":"journal_article","year":"2020","publisher":"Springer Nature","doi":"10.1007/s10955-019-02322-3","language":[{"iso":"eng"}],"article_type":"original","volume":180,"isi":1,"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"quality_controlled":"1","month":"09","intvolume":"       180","file_date_updated":"2020-11-19T11:13:55Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["510","530"],"article_processing_charge":"Yes (via OA deal)","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227; R.S.) is gratefully acknowledged.","department":[{"_id":"RoSe"}],"date_created":"2020-01-07T09:42:03Z"},{"date_updated":"2023-08-18T06:37:46Z","status":"public","ec_funded":1,"abstract":[{"text":"In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N d-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision in powers of N−1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.","lang":"eng"}],"page":"1362-1396","publication_status":"published","oa_version":"Published Version","day":"21","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02500-8\">https://doi.org/10.1007/s10955-020-02500-8</a>.","ieee":"L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections to the mean-field description of the dynamics of interacting bosons,” <i>Journal of Statistical Physics</i>, vol. 178. Springer Nature, pp. 1362–1396, 2020.","short":"L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics 178 (2020) 1362–1396.","mla":"Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>, vol. 178, Springer Nature, 2020, pp. 1362–96, doi:<a href=\"https://doi.org/10.1007/s10955-020-02500-8\">10.1007/s10955-020-02500-8</a>.","ista":"Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. 178, 1362–1396.","apa":"Bossmann, L., Pavlović, N., Pickl, P., &#38; Soffer, A. (2020). Higher order corrections to the mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02500-8\">https://doi.org/10.1007/s10955-020-02500-8</a>","ama":"Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical Physics</i>. 2020;178:1362-1396. doi:<a href=\"https://doi.org/10.1007/s10955-020-02500-8\">10.1007/s10955-020-02500-8</a>"},"arxiv":1,"has_accepted_license":"1","scopus_import":"1","external_id":{"arxiv":["1905.06164"],"isi":["000516342200001"]},"file":[{"file_size":576726,"file_name":"2020_JournStatPhysics_Bossmann.pdf","date_updated":"2020-11-20T09:26:46Z","success":1,"file_id":"8780","checksum":"643e230bf147e64d9cdb3f6cc573679d","date_created":"2020-11-20T09:26:46Z","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access"}],"title":"Higher order corrections to the mean-field description of the dynamics of interacting bosons","publication":"Journal of Statistical Physics","publisher":"Springer Nature","year":"2020","language":[{"iso":"eng"}],"doi":"10.1007/s10955-020-02500-8","type":"journal_article","oa":1,"_id":"7508","author":[{"first_name":"Lea","full_name":"Bossmann, Lea","last_name":"Bossmann","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","orcid":"0000-0002-6854-1343"},{"last_name":"Pavlović","full_name":"Pavlović, Nataša","first_name":"Nataša"},{"first_name":"Peter","full_name":"Pickl, Peter","last_name":"Pickl"},{"last_name":"Soffer","first_name":"Avy","full_name":"Soffer, Avy"}],"date_published":"2020-02-21T00:00:00Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\nL.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and wishes to thank Stefan Teufel, Sören Petrat and Marcello Porta for helpful discussions. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. N.P. gratefully acknowledges support from NSF grant DMS-1516228 and DMS-1840314. P.P.’s research was funded by DFG Grant no. PI 1114/3-1. Part of this work was done when N.P. and P.P. were visiting CCNU, Wuhan. N.P. and P.P. thank A.S. for his hospitality at CCNU.","department":[{"_id":"RoSe"}],"date_created":"2020-02-23T09:45:51Z","intvolume":"       178","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2020-11-20T09:26:46Z","quality_controlled":"1","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"month":"02","volume":178,"article_type":"original","isi":1},{"_id":"7514","oa":1,"author":[{"last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","first_name":"Simon","full_name":"Mayer, Simon"}],"date_published":"2020-02-24T00:00:00Z","year":"2020","publisher":"Institute of Science and Technology Austria","doi":"10.15479/AT:ISTA:7514","language":[{"iso":"eng"}],"type":"dissertation","publication_identifier":{"issn":["2663-337X"]},"month":"02","supervisor":[{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"}],"department":[{"_id":"RoSe"},{"_id":"GradSch"}],"date_created":"2020-02-24T09:17:27Z","file_date_updated":"2020-07-14T12:47:59Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","ddc":["510"],"degree_awarded":"PhD","abstract":[{"lang":"eng","text":"We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case.\r\nWe motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks."}],"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"24","oa_version":"Published Version","publication_status":"published","page":"148","date_updated":"2023-09-07T13:12:42Z","status":"public","file":[{"creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"thesis.pdf","file_size":1563429,"checksum":"b4de7579ddc1dbdd44ff3f17c48395f6","file_id":"7515","date_created":"2020-02-24T09:15:06Z","date_updated":"2020-07-14T12:47:59Z"},{"date_created":"2020-02-24T09:15:16Z","checksum":"ad7425867b52d7d9e72296e87bc9cb67","file_id":"7516","date_updated":"2020-07-14T12:47:59Z","file_name":"thesis_source.zip","file_size":2028038,"access_level":"closed","content_type":"application/x-zip-compressed","relation":"source_file","creator":"dernst"}],"title":"The free energy of a dilute two-dimensional Bose gas","related_material":{"record":[{"status":"public","id":"7524","relation":"part_of_dissertation"}]},"citation":{"short":"S. Mayer, The Free Energy of a Dilute Two-Dimensional Bose Gas, Institute of Science and Technology Austria, 2020.","ista":"Mayer S. 2020. The free energy of a dilute two-dimensional Bose gas. Institute of Science and Technology Austria.","mla":"Mayer, Simon. <i>The Free Energy of a Dilute Two-Dimensional Bose Gas</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7514\">10.15479/AT:ISTA:7514</a>.","apa":"Mayer, S. (2020). <i>The free energy of a dilute two-dimensional Bose gas</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7514\">https://doi.org/10.15479/AT:ISTA:7514</a>","ama":"Mayer S. The free energy of a dilute two-dimensional Bose gas. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7514\">10.15479/AT:ISTA:7514</a>","chicago":"Mayer, Simon. “The Free Energy of a Dilute Two-Dimensional Bose Gas.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7514\">https://doi.org/10.15479/AT:ISTA:7514</a>.","ieee":"S. Mayer, “The free energy of a dilute two-dimensional Bose gas,” Institute of Science and Technology Austria, 2020."},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"}],"has_accepted_license":"1","alternative_title":["ISTA Thesis"]},{"date_updated":"2023-09-05T15:14:50Z","status":"public","day":"12","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"page":"2143-2174","oa_version":"Published Version","publication_status":"published","abstract":[{"text":"We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.","lang":"eng"}],"ec_funded":1,"citation":{"chicago":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11005-020-01286-w\">https://doi.org/10.1007/s11005-020-01286-w</a>.","ieee":"S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through singular potentials,” <i>Letters in Mathematical Physics</i>, vol. 110. Springer Nature, pp. 2143–2174, 2020.","apa":"Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting through singular potentials. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01286-w\">https://doi.org/10.1007/s11005-020-01286-w</a>","ista":"Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics. 110, 2143–2174.","mla":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” <i>Letters in Mathematical Physics</i>, vol. 110, Springer Nature, 2020, pp. 2143–74, doi:<a href=\"https://doi.org/10.1007/s11005-020-01286-w\">10.1007/s11005-020-01286-w</a>.","short":"S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.","ama":"Rademacher SAE. Central limit theorem for Bose gases interacting through singular potentials. <i>Letters in Mathematical Physics</i>. 2020;110:2143-2174. doi:<a href=\"https://doi.org/10.1007/s11005-020-01286-w\">10.1007/s11005-020-01286-w</a>"},"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"scopus_import":"1","has_accepted_license":"1","publication":"Letters in Mathematical Physics","file":[{"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2020_LettersMathPhysics_Rademacher.pdf","file_size":478683,"checksum":"3bdd41f10ad947b67a45b98f507a7d4a","file_id":"8784","date_created":"2020-11-20T12:04:26Z","date_updated":"2020-11-20T12:04:26Z","success":1}],"title":"Central limit theorem for Bose gases interacting through singular potentials","external_id":{"isi":["000551556000006"]},"doi":"10.1007/s11005-020-01286-w","language":[{"iso":"eng"}],"year":"2020","publisher":"Springer Nature","type":"journal_article","author":[{"full_name":"Rademacher, Simone Anna Elvira","first_name":"Simone Anna Elvira","orcid":"0000-0001-5059-4466","last_name":"Rademacher","id":"856966FE-A408-11E9-977E-802DE6697425"}],"_id":"7611","oa":1,"date_published":"2020-03-12T00:00:00Z","date_created":"2020-03-23T11:11:47Z","department":[{"_id":"RoSe"}],"acknowledgement":"Simone Rademacher acknowledges partial support from the NCCR SwissMAP. This project has received\r\nfunding from the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R. would like to thank Benjamin Schlein for many fruitful discussions.","file_date_updated":"2020-11-20T12:04:26Z","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":"       110","month":"03","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"quality_controlled":"1","isi":1,"article_type":"original","volume":110},{"date_published":"2020-03-09T00:00:00Z","author":[{"first_name":"Andreas","full_name":"Deuchert, Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert"}],"oa":1,"_id":"7650","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00205-020-01489-4","publisher":"Springer Nature","year":"2020","isi":1,"article_type":"original","volume":236,"month":"03","quality_controlled":"1","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"file_date_updated":"2020-11-20T13:17:42Z","intvolume":"       236","date_created":"2020-04-08T15:18:03Z","department":[{"_id":"RoSe"}],"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_status":"published","page":"1217-1271","oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"09","ec_funded":1,"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."}],"status":"public","date_updated":"2023-09-05T14:18:49Z","publication":"Archive for Rational Mechanics and Analysis","external_id":{"isi":["000519415000001"],"arxiv":["1901.11363"]},"title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","file":[{"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","file_size":704633,"file_id":"8785","date_created":"2020-11-20T13:17:42Z","checksum":"b645fb64bfe95bbc05b3eea374109a9c","date_updated":"2020-11-20T13:17:42Z","success":1}],"issue":"6","scopus_import":"1","has_accepted_license":"1","project":[{"call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"citation":{"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.","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>.","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>","short":"A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236 (2020) 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>","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.","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>."},"arxiv":1},{"scopus_import":"1","issue":"1","citation":{"ama":"Lewin M, Lieb EH, Seiringer R.  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. 2020;2(1):35-73. doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2020).  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>","ista":"Lewin M, Lieb EH, Seiringer R. 2020.  The local density approximation in density functional theory. Pure and Applied Analysis. 2(1), 35–73.","mla":"Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>, vol. 2, no. 1, Mathematical Sciences Publishers, 2020, pp. 35–73, doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>.","short":"M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation in density functional theory,” <i>Pure and Applied Analysis</i>, vol. 2, no. 1. Mathematical Sciences Publishers, pp. 35–73, 2020.","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>."},"arxiv":1,"title":" The local density approximation in density functional theory","external_id":{"arxiv":["1903.04046"]},"publication":"Pure and Applied Analysis","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1903.04046"}],"status":"public","date_updated":"2024-01-29T09:01:12Z","abstract":[{"lang":"eng","text":"We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space."}],"day":"01","oa_version":"Preprint","publication_status":"published","page":"35-73","intvolume":"         2","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"date_created":"2024-01-28T23:01:44Z","volume":2,"article_type":"original","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"quality_controlled":"1","month":"01","type":"journal_article","year":"2020","publisher":"Mathematical Sciences Publishers","doi":"10.2140/paa.2020.2.35","language":[{"iso":"eng"}],"date_published":"2020-01-01T00:00:00Z","_id":"14891","oa":1,"author":[{"full_name":"Lewin, Mathieu","first_name":"Mathieu","last_name":"Lewin"},{"first_name":"Elliott H.","full_name":"Lieb, Elliott H.","last_name":"Lieb"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert"}]},{"department":[{"_id":"RoSe"}],"acknowledgement":"We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227.","date_created":"2021-08-06T07:34:16Z","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"intvolume":"        52","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"article_processing_charge":"No","quality_controlled":"1","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"month":"02","article_type":"original","volume":52,"isi":1,"publisher":"Society for Industrial & Applied Mathematics ","year":"2020","language":[{"iso":"eng"}],"doi":"10.1137/19m126284x","type":"journal_article","oa":1,"_id":"9781","author":[{"first_name":"Dario","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"date_published":"2020-02-12T00:00:00Z","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"citation":{"mla":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics , 2020, pp. 605–22, doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>.","short":"D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622.","apa":"Feliciangeli, D., &#38; Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics . <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>","ista":"Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622.","ama":"Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(1):605-622. doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>","chicago":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics , 2020. <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>.","ieee":"D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics , pp. 605–622, 2020."},"arxiv":1,"has_accepted_license":"1","issue":"1","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.08647"}],"related_material":{"record":[{"status":"public","id":"9733","relation":"dissertation_contains"}]},"external_id":{"arxiv":["1904.08647 "],"isi":["000546967700022"]},"title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball","publication":"SIAM Journal on Mathematical Analysis","date_updated":"2023-09-07T13:30:11Z","status":"public","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum."}],"page":"605-622","publication_status":"published","oa_version":"Preprint","tmp":{"image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"day":"12"},{"author":[{"id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert","orcid":"0000-0003-3146-6746","first_name":"Andreas","full_name":"Deuchert, Andreas"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"},{"last_name":"Yngvason","first_name":"Jakob","full_name":"Yngvason, Jakob"}],"_id":"80","oa":1,"date_published":"2019-06-01T00:00:00Z","doi":"10.1007/s00220-018-3239-0","language":[{"iso":"eng"}],"year":"2019","publisher":"Springer","type":"journal_article","month":"06","publist_id":"7974","quality_controlled":"1","isi":1,"article_type":"original","volume":368,"date_created":"2018-12-11T11:44:31Z","department":[{"_id":"RoSe"}],"file_date_updated":"2020-07-14T12:48:07Z","ddc":["530"],"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       368","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","page":"723-776","publication_status":"published","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer."}],"ec_funded":1,"date_updated":"2023-08-24T14:27:51Z","status":"public","publication":"Communications in Mathematical Physics","title":"Bose–Einstein condensation in a dilute, trapped gas at positive temperature","file":[{"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2018_CommunMathPhys_Deuchert.pdf","file_size":893902,"date_created":"2018-12-17T10:34:06Z","file_id":"5688","checksum":"c7e9880b43ac726712c1365e9f2f73a6","date_updated":"2020-07-14T12:48:07Z"}],"external_id":{"isi":["000467796800007"]},"citation":{"mla":"Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” <i>Communications in Mathematical Physics</i>, vol. 368, no. 2, Springer, 2019, pp. 723–76, doi:<a href=\"https://doi.org/10.1007/s00220-018-3239-0\">10.1007/s00220-018-3239-0</a>.","short":"A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 368 (2019) 723–776.","ista":"Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. 368(2), 723–776.","apa":"Deuchert, A., Seiringer, R., &#38; Yngvason, J. (2019). Bose–Einstein condensation in a dilute, trapped gas at positive temperature. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-018-3239-0\">https://doi.org/10.1007/s00220-018-3239-0</a>","ama":"Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. <i>Communications in Mathematical Physics</i>. 2019;368(2):723-776. doi:<a href=\"https://doi.org/10.1007/s00220-018-3239-0\">10.1007/s00220-018-3239-0</a>","chicago":"Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” <i>Communications in Mathematical Physics</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00220-018-3239-0\">https://doi.org/10.1007/s00220-018-3239-0</a>.","ieee":"A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in a dilute, trapped gas at positive temperature,” <i>Communications in Mathematical Physics</i>, vol. 368, no. 2. Springer, pp. 723–776, 2019."},"project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF"}],"scopus_import":"1","issue":"2","has_accepted_license":"1"},{"month":"10","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"quality_controlled":"1","isi":1,"volume":20,"article_type":"original","date_created":"2019-08-11T21:59:21Z","department":[{"_id":"RoSe"}],"file_date_updated":"2020-07-14T12:47:40Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"intvolume":"        20","author":[{"full_name":"Leopold, Nikolai K","first_name":"Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","last_name":"Leopold"},{"first_name":"Sören P","full_name":"Petrat, Sören P","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889"}],"_id":"6788","oa":1,"date_published":"2019-10-01T00:00:00Z","doi":"10.1007/s00023-019-00828-w","language":[{"iso":"eng"}],"year":"2019","publisher":"Springer Nature","type":"journal_article","publication":"Annales Henri Poincare","file":[{"creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","file_size":681139,"file_id":"6801","date_created":"2019-08-12T12:05:58Z","checksum":"b6dbf0d837d809293d449adf77138904","date_updated":"2020-07-14T12:47:40Z"}],"title":"Mean-field dynamics for the Nelson model with fermions","external_id":{"isi":["000487036900008"],"arxiv":["1807.06781"]},"citation":{"chicago":"Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>.","ieee":"N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature, pp. 3471–3508, 2019.","apa":"Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>","short":"N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.","mla":"Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>.","ista":"Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508.","ama":"Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>"},"arxiv":1,"project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"scopus_import":"1","issue":"10","has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","oa_version":"Published Version","publication_status":"published","page":"3471–3508","abstract":[{"lang":"eng","text":"We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations."}],"ec_funded":1,"date_updated":"2023-08-29T07:09:06Z","status":"public"},{"abstract":[{"lang":"eng","text":"We discuss thermodynamic properties of harmonically trapped\r\nimperfect quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition of the mean-field interparticle potential energy as compared\r\nto the homogeneous case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments that this model corresponds to the limiting case of\r\na long-ranged interparticle potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation similar to the well-known Kac scaling\r\nprocedure, which is presented here in a form adapted to the case of an isotropic\r\nharmonic trap. We show that within the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein condensation provided d > 1.\r\nThe main result of our analysis is that in d = 1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill\r\nthe relation aB + aF = \u001f. This result supplements similar recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform imperfect\r\nrepulsive Bose and attractive Fermi gases."}],"ec_funded":1,"day":"13","oa_version":"Preprint","publication_status":"published","status":"public","date_updated":"2023-08-29T07:19:13Z","title":"Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps","external_id":{"arxiv":["1810.02209"],"isi":["000471650100001"]},"publication":"Journal of Statistical Mechanics: Theory and Experiment","main_file_link":[{"url":"https://arxiv.org/abs/1810.02209","open_access":"1"}],"scopus_import":"1","issue":"6","arxiv":1,"citation":{"ieee":"K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019.","chicago":"Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2019. <a href=\"https://doi.org/10.1088/1742-5468/ab190d\">https://doi.org/10.1088/1742-5468/ab190d</a>.","ama":"Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2019;2019(6). doi:<a href=\"https://doi.org/10.1088/1742-5468/ab190d\">10.1088/1742-5468/ab190d</a>","apa":"Mysliwy, K., &#38; Napiórkowski, M. (2019). Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/ab190d\">https://doi.org/10.1088/1742-5468/ab190d</a>","ista":"Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063101.","short":"K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019).","mla":"Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:<a href=\"https://doi.org/10.1088/1742-5468/ab190d\">10.1088/1742-5468/ab190d</a>."},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020"}],"date_published":"2019-06-13T00:00:00Z","_id":"6840","oa":1,"author":[{"last_name":"Mysliwy","id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof","full_name":"Mysliwy, Krzysztof"},{"last_name":"Napiórkowski","first_name":"Marek","full_name":"Napiórkowski, Marek"}],"type":"journal_article","year":"2019","publisher":"IOP Publishing","doi":"10.1088/1742-5468/ab190d","language":[{"iso":"eng"}],"volume":2019,"isi":1,"publication_identifier":{"eissn":["1742-5468"]},"quality_controlled":"1","month":"06","intvolume":"      2019","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"RoSe"}],"date_created":"2019-09-01T22:00:59Z","article_number":"063101"},{"date_published":"2019-07-25T00:00:00Z","oa":1,"_id":"7015","author":[{"first_name":"Mathieu","full_name":"Lewin, Mathieu","last_name":"Lewin"},{"first_name":"Elliott H.","full_name":"Lieb, Elliott H.","last_name":"Lieb"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert"}],"type":"journal_article","publisher":"American Physical Society","year":"2019","language":[{"iso":"eng"}],"doi":"10.1103/physrevb.100.035127","article_type":"original","volume":100,"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["2469-9969"],"issn":["2469-9950"]},"month":"07","intvolume":"       100","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"date_created":"2019-11-13T08:41:48Z","article_number":"035127","ec_funded":1,"abstract":[{"text":"We modify the \"floating crystal\" trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential.","lang":"eng"}],"oa_version":"Preprint","publication_status":"published","day":"25","status":"public","date_updated":"2024-02-28T13:13:23Z","external_id":{"arxiv":["1905.09138"],"isi":["000477888200001"]},"title":"Floating Wigner crystal with no boundary charge fluctuations","publication":"Physical Review B","main_file_link":[{"url":"https://arxiv.org/abs/1905.09138","open_access":"1"}],"issue":"3","scopus_import":"1","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"citation":{"chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Floating Wigner Crystal with No Boundary Charge Fluctuations.” <i>Physical Review B</i>. American Physical Society, 2019. <a href=\"https://doi.org/10.1103/physrevb.100.035127\">https://doi.org/10.1103/physrevb.100.035127</a>.","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “Floating Wigner crystal with no boundary charge fluctuations,” <i>Physical Review B</i>, vol. 100, no. 3. American Physical Society, 2019.","short":"M. Lewin, E.H. Lieb, R. Seiringer, Physical Review B 100 (2019).","ista":"Lewin M, Lieb EH, Seiringer R. 2019. Floating Wigner crystal with no boundary charge fluctuations. Physical Review B. 100(3), 035127.","mla":"Lewin, Mathieu, et al. “Floating Wigner Crystal with No Boundary Charge Fluctuations.” <i>Physical Review B</i>, vol. 100, no. 3, 035127, American Physical Society, 2019, doi:<a href=\"https://doi.org/10.1103/physrevb.100.035127\">10.1103/physrevb.100.035127</a>.","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2019). Floating Wigner crystal with no boundary charge fluctuations. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevb.100.035127\">https://doi.org/10.1103/physrevb.100.035127</a>","ama":"Lewin M, Lieb EH, Seiringer R. Floating Wigner crystal with no boundary charge fluctuations. <i>Physical Review B</i>. 2019;100(3). doi:<a href=\"https://doi.org/10.1103/physrevb.100.035127\">10.1103/physrevb.100.035127</a>"},"arxiv":1},{"publication":"Communications in Mathematical Physics","external_id":{"isi":["000495193700002"]},"title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","file":[{"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"dernst","checksum":"cd283b475dd739e04655315abd46f528","date_created":"2019-11-25T08:11:11Z","file_id":"7101","date_updated":"2020-07-14T12:47:49Z","file_name":"2019_CommMathPhys_Jeblick.pdf","file_size":884469}],"issue":"1","scopus_import":"1","has_accepted_license":"1","project":[{"call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"citation":{"ieee":"M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent Gross–Pitaevskii equation in two dimensions,” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.","chicago":"Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>.","ama":"Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. 2019;372(1):1-69. doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>","apa":"Jeblick, M., Leopold, N. K., &#38; Pickl, P. (2019). Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>","ista":"Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69.","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69.","mla":"Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1, Springer Nature, 2019, pp. 1–69, doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>."},"publication_status":"published","oa_version":"Published Version","page":"1-69","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"08","ec_funded":1,"abstract":[{"text":"We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.","lang":"eng"}],"status":"public","date_updated":"2023-09-06T10:47:43Z","isi":1,"volume":372,"article_type":"original","month":"11","quality_controlled":"1","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_processing_charge":"Yes (via OA deal)","ddc":["510"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file_date_updated":"2020-07-14T12:47:49Z","intvolume":"       372","date_created":"2019-11-25T08:08:02Z","department":[{"_id":"RoSe"}],"acknowledgement":"OA fund by IST Austria","date_published":"2019-11-08T00:00:00Z","author":[{"full_name":"Jeblick, Maximilian","first_name":"Maximilian","last_name":"Jeblick"},{"orcid":"0000-0002-0495-6822","last_name":"Leopold","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","full_name":"Leopold, Nikolai K"},{"last_name":"Pickl","full_name":"Pickl, Peter","first_name":"Peter"}],"oa":1,"_id":"7100","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00220-019-03599-x","publisher":"Springer Nature","year":"2019"},{"language":[{"iso":"eng"}],"doi":"10.1063/1.5138135","publisher":"AIP Publishing","year":"2019","type":"journal_article","author":[{"last_name":"Jaksic","full_name":"Jaksic, Vojkan","first_name":"Vojkan"},{"first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"oa":1,"_id":"7226","date_published":"2019-12-01T00:00:00Z","article_number":"123504","date_created":"2020-01-05T23:00:46Z","department":[{"_id":"RoSe"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","ddc":["500"],"file_date_updated":"2020-07-14T12:47:54Z","intvolume":"        60","month":"12","quality_controlled":"1","publication_identifier":{"issn":["00222488"]},"isi":1,"article_type":"letter_note","volume":60,"date_updated":"2024-02-28T13:01:45Z","status":"public","publication_status":"published","oa_version":"Published Version","day":"01","citation":{"apa":"Jaksic, V., &#38; Seiringer, R. (2019). Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.5138135\">https://doi.org/10.1063/1.5138135</a>","short":"V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019).","ista":"Jaksic V, Seiringer R. 2019. Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics. 60(12), 123504.","mla":"Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018.” <i>Journal of Mathematical Physics</i>, vol. 60, no. 12, 123504, AIP Publishing, 2019, doi:<a href=\"https://doi.org/10.1063/1.5138135\">10.1063/1.5138135</a>.","ama":"Jaksic V, Seiringer R. Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. <i>Journal of Mathematical Physics</i>. 2019;60(12). doi:<a href=\"https://doi.org/10.1063/1.5138135\">10.1063/1.5138135</a>","chicago":"Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2019. <a href=\"https://doi.org/10.1063/1.5138135\">https://doi.org/10.1063/1.5138135</a>.","ieee":"V. Jaksic and R. Seiringer, “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018,” <i>Journal of Mathematical Physics</i>, vol. 60, no. 12. AIP Publishing, 2019."},"issue":"12","scopus_import":"1","has_accepted_license":"1","publication":"Journal of Mathematical Physics","external_id":{"isi":["000505529800002"]},"file":[{"file_name":"2019_JournalMathPhysics_Jaksic.pdf","file_size":1025015,"date_created":"2020-01-07T14:59:13Z","file_id":"7244","checksum":"bbd12ad1999a9ad7ba4d3c6f2e579c22","date_updated":"2020-07-14T12:47:54Z","creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"title":"Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018"},{"intvolume":"       222","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","department":[{"_id":"RoSe"}],"date_created":"2020-01-30T09:30:41Z","article_type":"original","volume":222,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["0001-5962"],"eissn":["1871-2509"]},"month":"06","type":"journal_article","publisher":"International Press of Boston","year":"2019","language":[{"iso":"eng"}],"doi":"10.4310/acta.2019.v222.n2.a1","date_published":"2019-06-07T00:00:00Z","oa":1,"_id":"7413","author":[{"full_name":"Boccato, Chiara","first_name":"Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","last_name":"Boccato"},{"last_name":"Brennecke","full_name":"Brennecke, Christian","first_name":"Christian"},{"last_name":"Cenatiempo","full_name":"Cenatiempo, Serena","first_name":"Serena"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"}],"issue":"2","scopus_import":"1","citation":{"apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2019). Bogoliubov theory in the Gross–Pitaevskii limit. <i>Acta Mathematica</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">https://doi.org/10.4310/acta.2019.v222.n2.a1</a>","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222 (2019) 219–335.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.","mla":"Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.” <i>Acta Mathematica</i>, vol. 222, no. 2, International Press of Boston, 2019, pp. 219–335, doi:<a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">10.4310/acta.2019.v222.n2.a1</a>.","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii limit. <i>Acta Mathematica</i>. 2019;222(2):219-335. doi:<a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">10.4310/acta.2019.v222.n2.a1</a>","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Bogoliubov Theory in the Gross–Pitaevskii Limit.” <i>Acta Mathematica</i>. International Press of Boston, 2019. <a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">https://doi.org/10.4310/acta.2019.v222.n2.a1</a>.","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory in the Gross–Pitaevskii limit,” <i>Acta Mathematica</i>, vol. 222, no. 2. International Press of Boston, pp. 219–335, 2019."},"arxiv":1,"external_id":{"isi":["000495865300001"],"arxiv":["1801.01389"]},"title":"Bogoliubov theory in the Gross–Pitaevskii limit","publication":"Acta Mathematica","main_file_link":[{"url":"https://arxiv.org/abs/1801.01389","open_access":"1"}],"status":"public","date_updated":"2023-09-06T15:24:31Z","abstract":[{"lang":"eng","text":"We consider Bose gases consisting of N particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of order N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s predictions."}],"publication_status":"published","oa_version":"Preprint","page":"219-335","day":"07"},{"scopus_import":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2020-02-26T08:46:40Z","department":[{"_id":"RoSe"}],"citation":{"chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv:1910.03372</i>. ArXiv, n.d.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>arXiv:1910.03372</i>. ArXiv.","short":"A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.).","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv:1910.03372</i>, ArXiv.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv:1910.03372</i>. ArXiv.","ista":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, .","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv:191003372</i>."},"project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"publication":"arXiv:1910.03372","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","related_material":{"record":[{"relation":"later_version","status":"public","id":"7790"},{"status":"public","id":"7514","relation":"dissertation_contains"}]},"month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.03372"}],"status":"public","type":"preprint","language":[{"iso":"eng"}],"year":"2019","date_updated":"2023-09-07T13:12:41Z","publisher":"ArXiv","day":"08","publication_status":"draft","oa_version":"Preprint","page":"61","date_published":"2019-10-08T00:00:00Z","abstract":[{"text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$ and inverse temperature $\\beta$ differs from the one of the non-interacting system by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ = \\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho \\ll 1$ and if $\\beta \\rho \\gtrsim 1$.","lang":"eng"}],"ec_funded":1,"author":[{"full_name":"Deuchert, Andreas","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert","orcid":"0000-0003-3146-6746"},{"first_name":"Simon","full_name":"Mayer, Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","last_name":"Mayer"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert"}],"_id":"7524","oa":1}]