{"publication":"arXiv","citation":{"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</i>. <a href=\"https://doi.org/10.48550/arXiv.1910.03372\">https://doi.org/10.48550/arXiv.1910.03372</a>","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.1910.03372\">10.48550/arXiv.1910.03372</a>","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.1910.03372\">https://doi.org/10.48550/arXiv.1910.03372</a>.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv</i>, 1910.03372, doi:<a href=\"https://doi.org/10.48550/arXiv.1910.03372\">10.48550/arXiv.1910.03372</a>.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>arXiv</i>. .","short":"A. Deuchert, S. Mayer, R. Seiringer, 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."},"arxiv":1,"_id":"7524","page":"61","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1910.03372","open_access":"1"}],"title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","OA_type":"green","oa":1,"date_updated":"2026-04-08T07:25:40Z","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.1910.03372","date_created":"2020-02-26T08:46:40Z","external_id":{"arxiv":["1910.03372"]},"article_number":"1910.03372","author":[{"id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","first_name":"Andreas","full_name":"Deuchert, Andreas","last_name":"Deuchert"},{"id":"30C4630A-F248-11E8-B48F-1D18A9856A87","first_name":"Simon","full_name":"Mayer, Simon","last_name":"Mayer"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"department":[{"_id":"RoSe"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"7790"},{"status":"public","relation":"dissertation_contains","id":"7514"}]},"ec_funded":1,"OA_place":"repository","fulldoi":"https://doi.org/10.48550/arXiv.1910.03372","corr_author":"1","day":"08","oa_version":"Preprint","publication_status":"draft","status":"public","date_published":"2019-10-08T00:00:00Z","type":"preprint","month":"10","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 $\\rho$ 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 $\\beta \\rho \\gtrsim 1$."}],"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","year":"2019"}