[{"department":[{"_id":"RoSe"}],"arxiv":1,"month":"05","citation":{"mla":"Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 1505–60, doi:<a href=\"https://doi.org/10.1007/s00023-022-01252-3\">10.1007/s00023-022-01252-3</a>.","apa":"Boccato, C., &#38; Seiringer, R. (2023). The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01252-3\">https://doi.org/10.1007/s00023-022-01252-3</a>","chicago":"Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01252-3\">https://doi.org/10.1007/s00023-022-01252-3</a>.","ista":"Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 24, 1505–1560.","short":"C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560.","ieee":"C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary conditions,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 1505–1560, 2023.","ama":"Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. 2023;24:1505-1560. doi:<a href=\"https://doi.org/10.1007/s00023-022-01252-3\">10.1007/s00023-022-01252-3</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"volume":24,"date_created":"2023-01-15T23:00:52Z","article_type":"original","scopus_import":"1","day":"01","author":[{"last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","full_name":"Boccato, Chiara","first_name":"Chiara"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"title":"The Bose Gas in a box with Neumann boundary conditions","oa_version":"Preprint","publication_identifier":{"issn":["1424-0637"]},"publication_status":"published","intvolume":"        24","abstract":[{"lang":"eng","text":"We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit."}],"year":"2023","isi":1,"external_id":{"isi":["000910751800002"],"arxiv":["2205.15284"]},"ec_funded":1,"date_published":"2023-05-01T00:00:00Z","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged.","status":"public","publication":"Annales Henri Poincare","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"_id":"12183","date_updated":"2023-08-16T11:34:03Z","type":"journal_article","article_processing_charge":"No","doi":"10.1007/s00023-022-01252-3","publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2205.15284","open_access":"1"}],"quality_controlled":"1","page":"1505-1560"},{"language":[{"iso":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"1","citation":{"ieee":"C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1. World Scientific, 2021.","short":"C. Boccato, Reviews in Mathematical Physics 33 (2021).","ama":"Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. <i>Reviews in Mathematical Physics</i>. 2021;33(1). doi:<a href=\"https://doi.org/10.1142/S0129055X20600065\">10.1142/S0129055X20600065</a>","apa":"Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. <i>Reviews in Mathematical Physics</i>. World Scientific. <a href=\"https://doi.org/10.1142/S0129055X20600065\">https://doi.org/10.1142/S0129055X20600065</a>","mla":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1, 2060006, World Scientific, 2021, doi:<a href=\"https://doi.org/10.1142/S0129055X20600065\">10.1142/S0129055X20600065</a>.","chicago":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” <i>Reviews in Mathematical Physics</i>. World Scientific, 2021. <a href=\"https://doi.org/10.1142/S0129055X20600065\">https://doi.org/10.1142/S0129055X20600065</a>.","ista":"Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 33(1), 2060006."},"arxiv":1,"month":"01","article_number":"2060006","department":[{"_id":"RoSe"}],"abstract":[{"text":"We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.","lang":"eng"}],"intvolume":"        33","publication_status":"published","publication_identifier":{"issn":["0129-055X"]},"title":"The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime","oa_version":"Preprint","author":[{"full_name":"Boccato, Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","last_name":"Boccato","first_name":"Chiara"}],"scopus_import":"1","day":"01","article_type":"original","date_created":"2020-04-26T22:00:45Z","volume":33,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"}],"publication":"Reviews in Mathematical Physics","status":"public","date_published":"2021-01-01T00:00:00Z","ec_funded":1,"external_id":{"arxiv":["2001.00497"],"isi":["000613313200007"]},"year":"2021","isi":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.00497"}],"publisher":"World Scientific","doi":"10.1142/S0129055X20600065","article_processing_charge":"No","type":"journal_article","date_updated":"2023-08-04T10:50:13Z","_id":"7685"},{"article_processing_charge":"No","doi":"10.4171/JEMS/966","publisher":"European Mathematical Society","_id":"8042","date_updated":"2023-08-22T07:47:04Z","type":"journal_article","page":"2331-2403","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.04819"}],"quality_controlled":"1","isi":1,"year":"2020","external_id":{"isi":["000548174700006"],"arxiv":["1704.04819"]},"status":"public","publication":"Journal of the European Mathematical Society","date_published":"2020-07-01T00:00:00Z","scopus_import":"1","day":"01","author":[{"id":"342E7E22-F248-11E8-B48F-1D18A9856A87","full_name":"Boccato, Chiara","last_name":"Boccato","first_name":"Chiara"},{"last_name":"Brennecke","full_name":"Brennecke, Christian","first_name":"Christian"},{"full_name":"Cenatiempo, Serena","last_name":"Cenatiempo","first_name":"Serena"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"}],"oa_version":"Preprint","title":"The excitation spectrum of Bose gases interacting through singular potentials","volume":22,"date_created":"2020-06-29T07:59:35Z","article_type":"original","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"}],"intvolume":"        22","publication_status":"published","publication_identifier":{"issn":["14359855"]},"month":"07","arxiv":1,"department":[{"_id":"RoSe"}],"oa":1,"language":[{"iso":"eng"}],"citation":{"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>.","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>.","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.","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."},"issue":"7","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"ec_funded":1,"date_published":"2020-06-01T00:00:00Z","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”.","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"publication":"Communications in Mathematical Physics","status":"public","isi":1,"year":"2020","external_id":{"isi":["000536053300012"],"arxiv":["1812.03086"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1812.03086"}],"quality_controlled":"1","page":"1311-1395","date_updated":"2024-02-22T13:33:02Z","_id":"6906","type":"journal_article","doi":"10.1007/s00220-019-03555-9","article_processing_charge":"No","publisher":"Springer","citation":{"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.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395.","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>","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>","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.","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>."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"arxiv":1,"month":"06","publication_status":"published","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"intvolume":"       376","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."}],"volume":376,"article_type":"original","date_created":"2019-09-24T17:30:59Z","author":[{"last_name":"Boccato","full_name":"Boccato, Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara"},{"first_name":"Christian","last_name":"Brennecke","full_name":"Brennecke, Christian"},{"first_name":"Serena","last_name":"Cenatiempo","full_name":"Cenatiempo, Serena"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"}],"scopus_import":"1","day":"01","title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","oa_version":"Preprint"},{"author":[{"last_name":"Boccato","full_name":"Boccato, Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara"},{"first_name":"Christian","full_name":"Brennecke, Christian","last_name":"Brennecke"},{"first_name":"Serena","full_name":"Cenatiempo, Serena","last_name":"Cenatiempo"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"}],"scopus_import":"1","day":"07","oa_version":"Preprint","title":"Bogoliubov theory in the Gross–Pitaevskii limit","volume":222,"article_type":"original","date_created":"2020-01-30T09:30:41Z","abstract":[{"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.","lang":"eng"}],"intvolume":"       222","publication_identifier":{"eissn":["1871-2509"],"issn":["0001-5962"]},"publication_status":"published","arxiv":1,"month":"06","department":[{"_id":"RoSe"}],"oa":1,"language":[{"iso":"eng"}],"issue":"2","citation":{"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.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222 (2019) 219–335.","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>","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>","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>.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.","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>."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.4310/acta.2019.v222.n2.a1","article_processing_charge":"No","publisher":"International Press of Boston","date_updated":"2023-09-06T15:24:31Z","_id":"7413","type":"journal_article","page":"219-335","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1801.01389"}],"quality_controlled":"1","isi":1,"year":"2019","external_id":{"isi":["000495865300001"],"arxiv":["1801.01389"]},"status":"public","publication":"Acta Mathematica","date_published":"2019-06-07T00:00:00Z"}]