[{"author":[{"id":"30C4630A-F248-11E8-B48F-1D18A9856A87","last_name":"Mayer","first_name":"Simon","full_name":"Mayer, Simon"}],"ddc":["510"],"date_published":"2020-02-24T00:00:00Z","oa_version":"Published Version","type":"dissertation","file_date_updated":"2020-07-14T12:47:59Z","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","doi":"10.15479/AT:ISTA:7514","publication_identifier":{"issn":["2663-337X"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","file":[{"file_size":1563429,"creator":"dernst","relation":"main_file","checksum":"b4de7579ddc1dbdd44ff3f17c48395f6","date_created":"2020-02-24T09:15:06Z","file_id":"7515","content_type":"application/pdf","date_updated":"2020-07-14T12:47:59Z","access_level":"open_access","file_name":"thesis.pdf"},{"file_size":2028038,"creator":"dernst","relation":"source_file","checksum":"ad7425867b52d7d9e72296e87bc9cb67","file_id":"7516","content_type":"application/x-zip-compressed","date_created":"2020-02-24T09:15:16Z","date_updated":"2020-07-14T12:47:59Z","access_level":"closed","file_name":"thesis_source.zip"}],"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"date_updated":"2023-09-07T13:12:42Z","year":"2020","date_created":"2020-02-24T09:17:27Z","page":"148","alternative_title":["ISTA Thesis"],"department":[{"_id":"RoSe"},{"_id":"GradSch"}],"publication_status":"published","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"7524"}]},"title":"The free energy of a dilute two-dimensional Bose gas","oa":1,"_id":"7514","month":"02","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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>","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>.","ista":"Mayer S. 2020. The free energy of a dilute two-dimensional Bose gas. Institute of Science and Technology Austria.","ieee":"S. Mayer, “The free energy of a dilute two-dimensional Bose gas,” Institute of Science and Technology Austria, 2020.","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>.","short":"S. Mayer, The Free Energy of a Dilute Two-Dimensional Bose Gas, Institute of Science and Technology Austria, 2020.","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>"},"supervisor":[{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"has_accepted_license":"1","day":"24","abstract":[{"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.","lang":"eng"}],"status":"public","ec_funded":1,"degree_awarded":"PhD"},{"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.","department":[{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"03","_id":"7611","article_type":"original","oa":1,"title":"Central limit theorem for Bose gases interacting through singular potentials","publication_status":"published","has_accepted_license":"1","day":"12","citation":{"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.","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>.","ista":"Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics. 110, 2143–2174.","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>.","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>","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>","short":"S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174."},"intvolume":"       110","ec_funded":1,"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"}],"status":"public","date_published":"2020-03-12T00:00:00Z","external_id":{"isi":["000551556000006"]},"oa_version":"Published Version","ddc":["510"],"author":[{"id":"856966FE-A408-11E9-977E-802DE6697425","orcid":"0000-0001-5059-4466","first_name":"Simone Anna Elvira","full_name":"Rademacher, Simone Anna Elvira","last_name":"Rademacher"}],"publication":"Letters in Mathematical Physics","publisher":"Springer Nature","doi":"10.1007/s11005-020-01286-w","file_date_updated":"2020-11-20T12:04:26Z","type":"journal_article","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"date_updated":"2023-09-05T15:14:50Z","project":[{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"2143-2174","quality_controlled":"1","date_created":"2020-03-23T11:11:47Z","year":"2020","volume":110,"isi":1,"file":[{"relation":"main_file","checksum":"3bdd41f10ad947b67a45b98f507a7d4a","file_size":478683,"creator":"dernst","file_name":"2020_LettersMathPhysics_Rademacher.pdf","date_created":"2020-11-20T12:04:26Z","file_id":"8784","content_type":"application/pdf","date_updated":"2020-11-20T12:04:26Z","success":1,"access_level":"open_access"}]},{"doi":"10.1007/s00205-020-01489-4","publisher":"Springer Nature","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","file_date_updated":"2020-11-20T13:17:42Z","external_id":{"isi":["000519415000001"],"arxiv":["1901.11363"]},"oa_version":"Published Version","date_published":"2020-03-09T00:00:00Z","publication":"Archive for Rational Mechanics and Analysis","issue":"6","author":[{"last_name":"Deuchert","first_name":"Andreas","full_name":"Deuchert, Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"ddc":["510"],"year":"2020","date_created":"2020-04-08T15:18:03Z","quality_controlled":"1","page":"1217-1271","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"date_updated":"2023-09-05T14:18:49Z","file":[{"checksum":"b645fb64bfe95bbc05b3eea374109a9c","relation":"main_file","creator":"dernst","file_size":704633,"file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","access_level":"open_access","success":1,"date_updated":"2020-11-20T13:17:42Z","date_created":"2020-11-20T13:17:42Z","file_id":"8785","content_type":"application/pdf"}],"isi":1,"volume":236,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"scopus_import":"1","month":"03","_id":"7650","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_status":"published","oa":1,"title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","article_type":"original","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.","ec_funded":1,"status":"public","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."}],"day":"09","has_accepted_license":"1","citation":{"ama":"Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271. doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>","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.","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>.","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."},"intvolume":"       236"},{"arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","file_date_updated":"2020-07-14T12:48:03Z","doi":"10.1017/fms.2020.17","publisher":"Cambridge University Press","publication":"Forum of Mathematics, Sigma","author":[{"id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","first_name":"Andreas","full_name":"Deuchert, Andreas","last_name":"Deuchert"},{"full_name":"Mayer, Simon","first_name":"Simon","last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"}],"ddc":["510"],"oa_version":"Published Version","external_id":{"isi":["000527342000001"],"arxiv":["1910.03372"]},"date_published":"2020-03-14T00:00:00Z","isi":1,"file":[{"access_level":"open_access","date_updated":"2020-07-14T12:48:03Z","content_type":"application/pdf","date_created":"2020-05-04T12:02:41Z","file_id":"7797","file_name":"2020_ForumMath_Deuchert.pdf","creator":"dernst","file_size":692530,"checksum":"8a64da99d107686997876d7cad8cfe1e","relation":"main_file"}],"volume":8,"date_created":"2020-05-03T22:00:48Z","year":"2020","quality_controlled":"1","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"date_updated":"2023-08-21T06:18:49Z","publication_identifier":{"eissn":["20505094"]},"scopus_import":"1","article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication_status":"published","related_material":{"record":[{"id":"7524","status":"public","relation":"earlier_version"}]},"oa":1,"title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","article_type":"original","_id":"7790","month":"03","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"RoSe"}],"status":"public","article_number":"e20","abstract":[{"lang":"eng","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 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 ."}],"ec_funded":1,"citation":{"ista":"Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020.","short":"A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>"},"intvolume":"         8","day":"14","has_accepted_license":"1"},{"article_processing_charge":"No","publication_identifier":{"issn":["14359855"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.04819"}],"scopus_import":"1","year":"2020","date_created":"2020-06-29T07:59:35Z","page":"2331-2403","quality_controlled":"1","date_updated":"2023-08-22T07:47:04Z","isi":1,"volume":22,"external_id":{"arxiv":["1704.04819"],"isi":["000548174700006"]},"oa_version":"Preprint","date_published":"2020-07-01T00:00:00Z","issue":"7","publication":"Journal of the European Mathematical Society","author":[{"id":"342E7E22-F248-11E8-B48F-1D18A9856A87","full_name":"Boccato, Chiara","first_name":"Chiara","last_name":"Boccato"},{"last_name":"Brennecke","full_name":"Brennecke, Christian","first_name":"Christian"},{"first_name":"Serena","full_name":"Cenatiempo, Serena","last_name":"Cenatiempo"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"}],"doi":"10.4171/JEMS/966","publisher":"European Mathematical Society","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","day":"01","citation":{"mla":"Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” <i>Journal of the European Mathematical Society</i>, vol. 22, no. 7, European Mathematical Society, 2020, pp. 2331–403, doi:<a href=\"https://doi.org/10.4171/JEMS/966\">10.4171/JEMS/966</a>.","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum of Bose gases interacting through singular potentials,” <i>Journal of the European Mathematical Society</i>, vol. 22, no. 7. European Mathematical Society, pp. 2331–2403, 2020.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. The excitation spectrum of Bose gases interacting through singular potentials. Journal of the European Mathematical Society. 22(7), 2331–2403.","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society, 2020. <a href=\"https://doi.org/10.4171/JEMS/966\">https://doi.org/10.4171/JEMS/966</a>.","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). The excitation spectrum of Bose gases interacting through singular potentials. <i>Journal of the European Mathematical Society</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/JEMS/966\">https://doi.org/10.4171/JEMS/966</a>","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of Bose gases interacting through singular potentials. <i>Journal of the European Mathematical Society</i>. 2020;22(7):2331-2403. doi:<a href=\"https://doi.org/10.4171/JEMS/966\">10.4171/JEMS/966</a>","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European Mathematical Society 22 (2020) 2331–2403."},"intvolume":"        22","status":"public","abstract":[{"text":"We consider systems of N bosons in a box of volume one, interacting through a repulsive two-body potential of the form κN3β−1V(Nβx). For all 0<β<1, and for sufficiently small coupling constant κ>0, we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large N.","lang":"eng"}],"department":[{"_id":"RoSe"}],"_id":"8042","month":"07","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","oa":1,"title":"The excitation spectrum of Bose gases interacting through singular potentials","article_type":"original"},{"citation":{"ieee":"R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” <i>Journal of Statistical Physics</i>, vol. 181. Springer, pp. 448–464, 2020.","mla":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>, vol. 181, Springer, 2020, pp. 448–64, doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>.","apa":"Seiringer, R., &#38; Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>","chicago":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>.","ista":"Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464.","ama":"Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. 2020;181:448-464. doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>","short":"R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464."},"intvolume":"       181","day":"01","has_accepted_license":"1","status":"public","abstract":[{"lang":"eng","text":"In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane’s pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in [6], which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level."}],"ec_funded":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\nThe work of R.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. ","department":[{"_id":"RoSe"}],"title":"Emergence of Haldane pseudo-potentials in systems with short-range interactions","oa":1,"publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"10","_id":"8091","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":181,"isi":1,"file":[{"relation":"main_file","checksum":"5cbeef52caf18d0d952f17fed7b5545a","file_size":404778,"creator":"dernst","file_name":"2020_JourStatPhysics_Seiringer.pdf","file_id":"8812","content_type":"application/pdf","date_created":"2020-11-25T15:05:04Z","success":1,"access_level":"open_access","date_updated":"2020-11-25T15:05:04Z"}],"page":"448-464","quality_controlled":"1","year":"2020","date_created":"2020-07-05T22:00:46Z","date_updated":"2023-08-22T07:51:47Z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"publication":"Journal of Statistical Physics","ddc":["530"],"author":[{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"},{"full_name":"Yngvason, Jakob","first_name":"Jakob","last_name":"Yngvason"}],"external_id":{"arxiv":["2001.07144"],"isi":["000543030000002"]},"oa_version":"Published Version","date_published":"2020-10-01T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2020-11-25T15:05:04Z","type":"journal_article","doi":"10.1007/s10955-020-02586-0","publisher":"Springer"},{"ec_funded":1,"status":"public","abstract":[{"lang":"eng","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."}],"day":"01","has_accepted_license":"1","intvolume":"       238","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.","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>.","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>.","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>","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>","short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"11","_id":"8130","title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","oa":1,"publication_status":"published","article_type":"original","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.","department":[{"_id":"RoSe"}],"quality_controlled":"1","page":"541-606","date_created":"2020-07-18T15:06:35Z","year":"2020","date_updated":"2023-09-05T14:19:06Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"volume":238,"isi":1,"file":[{"file_id":"8826","date_created":"2020-12-02T08:50:38Z","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-12-02T08:50:38Z","success":1,"file_name":"2020_ArchiveRatMech_Bossmann.pdf","file_size":942343,"creator":"dernst","relation":"main_file","checksum":"cc67a79a67bef441625fcb1cd031db3d"}],"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"scopus_import":"1","doi":"10.1007/s00205-020-01548-w","publisher":"Springer Nature","language":[{"iso":"eng"}],"arxiv":1,"file_date_updated":"2020-12-02T08:50:38Z","type":"journal_article","external_id":{"arxiv":["1907.04547"],"isi":["000550164400001"]},"oa_version":"Published Version","date_published":"2020-11-01T00:00:00Z","publication":"Archive for Rational Mechanics and Analysis","issue":"11","ddc":["510"],"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","orcid":"0000-0002-6854-1343","first_name":"Lea","full_name":"Bossmann, Lea","last_name":"Bossmann"}]},{"department":[{"_id":"RoSe"}],"article_type":"original","oa":1,"title":"The free energy of the two-dimensional dilute Bose gas. II. Upper bound","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8134","month":"06","citation":{"ama":"Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. 2020;61(6). doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>","short":"S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).","ieee":"S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. II. Upper bound,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6. AIP Publishing, 2020.","mla":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6, 061901, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>.","apa":"Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>","chicago":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>.","ista":"Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901."},"intvolume":"        61","day":"22","abstract":[{"lang":"eng","text":"We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality in the asymptotic expansion."}],"article_number":"061901","status":"public","ec_funded":1,"author":[{"id":"30C4630A-F248-11E8-B48F-1D18A9856A87","first_name":"Simon","full_name":"Mayer, Simon","last_name":"Mayer"},{"first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"issue":"6","publication":"Journal of Mathematical Physics","date_published":"2020-06-22T00:00:00Z","external_id":{"isi":["000544595100001"],"arxiv":["2002.08281"]},"oa_version":"Preprint","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"publisher":"AIP Publishing","doi":"10.1063/5.0005950","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2002.08281","open_access":"1"}],"publication_identifier":{"issn":["00222488"]},"article_processing_charge":"No","volume":61,"isi":1,"date_updated":"2023-08-22T08:12:40Z","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","date_created":"2020-07-19T22:00:59Z","year":"2020"},{"publisher":"Mathematical Sciences Publishers","doi":"10.2140/paa.2020.2.35","type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"date_published":"2020-01-01T00:00:00Z","oa_version":"Preprint","external_id":{"arxiv":["1903.04046"]},"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","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"publication":"Pure and Applied Analysis","issue":"1","date_updated":"2024-01-29T09:01:12Z","year":"2020","date_created":"2024-01-28T23:01:44Z","quality_controlled":"1","page":"35-73","volume":2,"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1903.04046"}],"scopus_import":"1","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"_id":"14891","month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","publication_status":"published","title":" The local density approximation in density functional theory","oa":1,"department":[{"_id":"RoSe"}],"abstract":[{"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.","lang":"eng"}],"status":"public","day":"01","citation":{"short":"M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.","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>","ista":"Lewin M, Lieb EH, Seiringer R. 2020.  The local density approximation in density functional theory. Pure and Applied Analysis. 2(1), 35–73.","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>.","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>","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.","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>."},"intvolume":"         2"},{"ec_funded":1,"status":"public","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"}],"day":"01","has_accepted_license":"1","intvolume":"       374","citation":{"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>","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>.","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.","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>.","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.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","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>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6649","month":"03","oa":1,"title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","publication_status":"published","article_type":"original","department":[{"_id":"RoSe"}],"quality_controlled":"1","page":"2097–2150","date_created":"2019-07-18T13:30:04Z","year":"2020","date_updated":"2023-08-17T13:51:50Z","project":[{"name":"FWF Open Access Fund","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","call_identifier":"FWF"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"volume":374,"file":[{"creator":"dernst","file_size":853289,"checksum":"f9dd6dd615a698f1d3636c4a092fed23","relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:47:35Z","content_type":"application/pdf","date_created":"2019-07-24T07:19:10Z","file_id":"6668","file_name":"2019_CommMathPhysics_Benedikter.pdf"}],"isi":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"scopus_import":"1","doi":"10.1007/s00220-019-03505-5","publisher":"Springer Nature","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:35Z","type":"journal_article","external_id":{"arxiv":["1809.01902"],"isi":["000527910700019"]},"oa_version":"Published Version","date_published":"2020-03-01T00:00:00Z","publication":"Communications in Mathematical Physics","ddc":["530"],"author":[{"orcid":"0000-0002-1071-6091","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","full_name":"Benedikter, Niels P","first_name":"Niels P","last_name":"Benedikter"},{"full_name":"Nam, Phan Thành","first_name":"Phan Thành","last_name":"Nam"},{"full_name":"Porta, Marcello","first_name":"Marcello","last_name":"Porta"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}]},{"isi":1,"volume":376,"year":"2020","date_created":"2019-09-24T17:30:59Z","quality_controlled":"1","page":"1311-1395","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"date_updated":"2024-02-22T13:33:02Z","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"main_file_link":[{"url":"https://arxiv.org/abs/1812.03086","open_access":"1"}],"scopus_import":"1","article_processing_charge":"No","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","doi":"10.1007/s00220-019-03555-9","publisher":"Springer","publication":"Communications in Mathematical Physics","author":[{"full_name":"Boccato, Chiara","first_name":"Chiara","last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Brennecke","first_name":"Christian","full_name":"Brennecke, Christian"},{"last_name":"Cenatiempo","first_name":"Serena","full_name":"Cenatiempo, Serena"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"}],"external_id":{"isi":["000536053300012"],"arxiv":["1812.03086"]},"oa_version":"Preprint","date_published":"2020-06-01T00:00:00Z","status":"public","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"citation":{"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>.","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.","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>.","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>","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395."},"intvolume":"       376","day":"01","publication_status":"published","oa":1,"title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","article_type":"original","_id":"6906","month":"06","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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"}]},{"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"main_file_link":[{"url":"https://arxiv.org/abs/1904.08647","open_access":"1"}],"scopus_import":"1","article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)"},"isi":1,"volume":52,"date_created":"2021-08-06T07:34:16Z","year":"2020","page":"605-622","quality_controlled":"1","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"date_updated":"2023-09-07T13:30:11Z","publication":"SIAM Journal on Mathematical Analysis","issue":"1","author":[{"last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","first_name":"Dario","orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert"}],"ddc":["510"],"oa_version":"Preprint","external_id":{"isi":["000546967700022"],"arxiv":["1904.08647 "]},"date_published":"2020-02-12T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","doi":"10.1137/19m126284x","publisher":"Society for Industrial & Applied Mathematics ","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"citation":{"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>","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>.","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.","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.","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.","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>"},"intvolume":"        52","day":"12","has_accepted_license":"1","status":"public","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"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.","department":[{"_id":"RoSe"}],"publication_status":"published","oa":1,"title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball","related_material":{"record":[{"id":"9733","relation":"dissertation_contains","status":"public"}]},"article_type":"original","month":"02","_id":"9781","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"publisher":"American Physical Society","doi":"10.1103/physrevb.100.035127","author":[{"last_name":"Lewin","first_name":"Mathieu","full_name":"Lewin, Mathieu"},{"last_name":"Lieb","full_name":"Lieb, Elliott H.","first_name":"Elliott H."},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"issue":"3","publication":"Physical Review B","date_published":"2019-07-25T00:00:00Z","external_id":{"isi":["000477888200001"],"arxiv":["1905.09138"]},"oa_version":"Preprint","volume":100,"isi":1,"date_updated":"2024-02-28T13:13:23Z","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"quality_controlled":"1","year":"2019","date_created":"2019-11-13T08:41:48Z","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1905.09138","open_access":"1"}],"publication_identifier":{"issn":["2469-9950"],"eissn":["2469-9969"]},"article_processing_charge":"No","article_type":"original","title":"Floating Wigner crystal with no boundary charge fluctuations","oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","_id":"7015","department":[{"_id":"RoSe"}],"abstract":[{"lang":"eng","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."}],"article_number":"035127","status":"public","ec_funded":1,"intvolume":"       100","citation":{"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>.","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.","ista":"Lewin M, Lieb EH, Seiringer R. 2019. Floating Wigner crystal with no boundary charge fluctuations. Physical Review B. 100(3), 035127.","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>","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>.","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>","short":"M. Lewin, E.H. Lieb, R. Seiringer, Physical Review B 100 (2019)."},"day":"25"},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_updated":"2023-09-06T10:47:43Z","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"page":"1-69","quality_controlled":"1","year":"2019","date_created":"2019-11-25T08:08:02Z","volume":372,"isi":1,"file":[{"date_created":"2019-11-25T08:11:11Z","file_id":"7101","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:49Z","file_name":"2019_CommMathPhys_Jeblick.pdf","file_size":884469,"creator":"dernst","relation":"main_file","checksum":"cd283b475dd739e04655315abd46f528"}],"date_published":"2019-11-08T00:00:00Z","external_id":{"isi":["000495193700002"]},"oa_version":"Published Version","ddc":["510"],"author":[{"full_name":"Jeblick, Maximilian","first_name":"Maximilian","last_name":"Jeblick"},{"orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","last_name":"Leopold"},{"full_name":"Pickl, Peter","first_name":"Peter","last_name":"Pickl"}],"publication":"Communications in Mathematical Physics","issue":"1","publisher":"Springer Nature","doi":"10.1007/s00220-019-03599-x","file_date_updated":"2020-07-14T12:47:49Z","type":"journal_article","language":[{"iso":"eng"}],"has_accepted_license":"1","day":"08","intvolume":"       372","citation":{"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>.","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>.","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.","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>","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>","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69."},"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","acknowledgement":"OA fund by IST Austria","department":[{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"7100","month":"11","article_type":"original","oa":1,"title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","publication_status":"published"},{"has_accepted_license":"1","day":"01","citation":{"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>","short":"V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019).","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.","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>.","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.","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>.","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>"},"intvolume":"        60","status":"public","article_number":"123504","department":[{"_id":"RoSe"}],"month":"12","_id":"7226","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"letter_note","publication_status":"published","oa":1,"title":"Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018","article_processing_charge":"No","scopus_import":"1","publication_identifier":{"issn":["00222488"]},"date_updated":"2024-02-28T13:01:45Z","year":"2019","date_created":"2020-01-05T23:00:46Z","quality_controlled":"1","isi":1,"file":[{"checksum":"bbd12ad1999a9ad7ba4d3c6f2e579c22","relation":"main_file","creator":"dernst","file_size":1025015,"file_name":"2019_JournalMathPhysics_Jaksic.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:54Z","file_id":"7244","content_type":"application/pdf","date_created":"2020-01-07T14:59:13Z"}],"volume":60,"date_published":"2019-12-01T00:00:00Z","external_id":{"isi":["000505529800002"]},"oa_version":"Published Version","author":[{"full_name":"Jaksic, Vojkan","first_name":"Vojkan","last_name":"Jaksic"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"ddc":["500"],"publication":"Journal of Mathematical Physics","issue":"12","publisher":"AIP Publishing","doi":"10.1063/1.5138135","type":"journal_article","file_date_updated":"2020-07-14T12:47:54Z","language":[{"iso":"eng"}]},{"day":"07","citation":{"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>.","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.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.","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>","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>.","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>","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222 (2019) 219–335."},"intvolume":"       222","status":"public","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."}],"department":[{"_id":"RoSe"}],"month":"06","_id":"7413","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_status":"published","oa":1,"title":"Bogoliubov theory in the Gross–Pitaevskii limit","article_type":"original","article_processing_charge":"No","publication_identifier":{"eissn":["1871-2509"],"issn":["0001-5962"]},"main_file_link":[{"url":"https://arxiv.org/abs/1801.01389","open_access":"1"}],"scopus_import":"1","date_created":"2020-01-30T09:30:41Z","year":"2019","quality_controlled":"1","page":"219-335","date_updated":"2023-09-06T15:24:31Z","isi":1,"volume":222,"external_id":{"isi":["000495865300001"],"arxiv":["1801.01389"]},"oa_version":"Preprint","date_published":"2019-06-07T00:00:00Z","issue":"2","publication":"Acta Mathematica","author":[{"last_name":"Boccato","full_name":"Boccato, Chiara","first_name":"Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Brennecke","first_name":"Christian","full_name":"Brennecke, Christian"},{"last_name":"Cenatiempo","first_name":"Serena","full_name":"Cenatiempo, Serena"},{"last_name":"Schlein","full_name":"Schlein, Benjamin","first_name":"Benjamin"}],"doi":"10.4310/acta.2019.v222.n2.a1","publisher":"International Press of Boston","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article"},{"publisher":"ArXiv","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7524","month":"10","type":"preprint","oa":1,"title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","related_material":{"record":[{"status":"public","relation":"later_version","id":"7790"},{"status":"public","relation":"dissertation_contains","id":"7514"}]},"language":[{"iso":"eng"}],"publication_status":"draft","date_published":"2019-10-08T00:00:00Z","department":[{"_id":"RoSe"}],"oa_version":"Preprint","author":[{"id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","last_name":"Deuchert","first_name":"Andreas","full_name":"Deuchert, Andreas"},{"id":"30C4630A-F248-11E8-B48F-1D18A9856A87","full_name":"Mayer, Simon","first_name":"Simon","last_name":"Mayer"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"publication":"arXiv:1910.03372","date_updated":"2023-09-07T13:12:41Z","ec_funded":1,"project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"page":"61","year":"2019","date_created":"2020-02-26T08:46:40Z","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"}],"status":"public","article_processing_charge":"No","day":"08","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.03372"}],"citation":{"short":"A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.).","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv:191003372</i>.","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.","ista":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, .","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.","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.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv:1910.03372</i>, ArXiv."}},{"ec_funded":1,"abstract":[{"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.","lang":"eng"}],"status":"public","has_accepted_license":"1","day":"01","citation":{"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>","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>.","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>.","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.","short":"A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 368 (2019) 723–776.","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>"},"intvolume":"       368","month":"06","_id":"80","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","publication_status":"published","title":"Bose–Einstein condensation in a dilute, trapped gas at positive temperature","oa":1,"department":[{"_id":"RoSe"}],"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF"}],"date_updated":"2023-08-24T14:27:51Z","year":"2019","date_created":"2018-12-11T11:44:31Z","quality_controlled":"1","page":"723-776","file":[{"content_type":"application/pdf","file_id":"5688","date_created":"2018-12-17T10:34:06Z","access_level":"open_access","date_updated":"2020-07-14T12:48:07Z","file_name":"2018_CommunMathPhys_Deuchert.pdf","file_size":893902,"creator":"dernst","relation":"main_file","checksum":"c7e9880b43ac726712c1365e9f2f73a6"}],"isi":1,"volume":368,"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","publisher":"Springer","doi":"10.1007/s00220-018-3239-0","type":"journal_article","file_date_updated":"2020-07-14T12:48:07Z","language":[{"iso":"eng"}],"date_published":"2019-06-01T00:00:00Z","external_id":{"isi":["000467796800007"]},"oa_version":"Published Version","author":[{"last_name":"Deuchert","full_name":"Deuchert, Andreas","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jakob","full_name":"Yngvason, Jakob","last_name":"Yngvason"}],"ddc":["530"],"issue":"2","publist_id":"7974","publication":"Communications in Mathematical Physics"},{"publisher":"Springer","doi":"10.1007/s00023-018-00757-0","file_date_updated":"2020-07-14T12:47:12Z","type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"date_published":"2019-04-01T00:00:00Z","oa_version":"Published Version","external_id":{"arxiv":["1807.00739"],"isi":["000462444300008"]},"ddc":["530"],"author":[{"id":"2B5FC9A4-F248-11E8-B48F-1D18A9856A87","last_name":"Moser","first_name":"Thomas","full_name":"Moser, Thomas"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"issue":"4","publication":"Annales Henri Poincare","date_updated":"2023-09-07T12:37:42Z","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"page":"1325–1365","quality_controlled":"1","year":"2019","date_created":"2019-01-20T22:59:17Z","volume":20,"isi":1,"file":[{"file_name":"2019_Annales_Moser.pdf","date_created":"2019-01-28T15:27:17Z","file_id":"5894","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:12Z","relation":"main_file","checksum":"255e42f957a8e2b10aad2499c750a8d6","file_size":859846,"creator":"dernst"}],"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","publication_identifier":{"issn":["14240637"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"04","_id":"5856","article_type":"original","title":"Energy contribution of a point-interacting impurity in a Fermi gas","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"52"}]},"oa":1,"publication_status":"published","department":[{"_id":"RoSe"}],"ec_funded":1,"abstract":[{"lang":"eng","text":"We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of N. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently showed stability of the system."}],"status":"public","has_accepted_license":"1","day":"01","citation":{"ieee":"T. Moser and R. Seiringer, “Energy contribution of a point-interacting impurity in a Fermi gas,” <i>Annales Henri Poincare</i>, vol. 20, no. 4. Springer, pp. 1325–1365, 2019.","mla":"Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting Impurity in a Fermi Gas.” <i>Annales Henri Poincare</i>, vol. 20, no. 4, Springer, 2019, pp. 1325–1365, doi:<a href=\"https://doi.org/10.1007/s00023-018-00757-0\">10.1007/s00023-018-00757-0</a>.","apa":"Moser, T., &#38; Seiringer, R. (2019). Energy contribution of a point-interacting impurity in a Fermi gas. <i>Annales Henri Poincare</i>. Springer. <a href=\"https://doi.org/10.1007/s00023-018-00757-0\">https://doi.org/10.1007/s00023-018-00757-0</a>","ista":"Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365.","chicago":"Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting Impurity in a Fermi Gas.” <i>Annales Henri Poincare</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00023-018-00757-0\">https://doi.org/10.1007/s00023-018-00757-0</a>.","ama":"Moser T, Seiringer R. Energy contribution of a point-interacting impurity in a Fermi gas. <i>Annales Henri Poincare</i>. 2019;20(4):1325–1365. doi:<a href=\"https://doi.org/10.1007/s00023-018-00757-0\">10.1007/s00023-018-00757-0</a>","short":"T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365."},"intvolume":"        20"},{"abstract":[{"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.","lang":"eng"}],"status":"public","ec_funded":1,"intvolume":"        20","citation":{"short":"N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 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>","ista":"Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508.","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>","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.","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>."},"has_accepted_license":"1","day":"01","article_type":"original","oa":1,"title":"Mean-field dynamics for the Nelson model with fermions","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"10","_id":"6788","department":[{"_id":"RoSe"}],"volume":20,"isi":1,"file":[{"date_created":"2019-08-12T12:05:58Z","content_type":"application/pdf","file_id":"6801","access_level":"open_access","date_updated":"2020-07-14T12:47:40Z","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","file_size":681139,"creator":"dernst","relation":"main_file","checksum":"b6dbf0d837d809293d449adf77138904"}],"date_updated":"2023-08-29T07:09:06Z","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","page":"3471–3508","year":"2019","date_created":"2019-08-11T21:59:21Z","scopus_import":"1","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file_date_updated":"2020-07-14T12:47:40Z","type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"publisher":"Springer Nature","doi":"10.1007/s00023-019-00828-w","ddc":["510"],"author":[{"orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","last_name":"Leopold"},{"last_name":"Petrat","full_name":"Petrat, Sören P","first_name":"Sören P","orcid":"0000-0002-9166-5889","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"}],"publication":"Annales Henri Poincare","issue":"10","date_published":"2019-10-01T00:00:00Z","external_id":{"arxiv":["1807.06781"],"isi":["000487036900008"]},"oa_version":"Published Version"}]