{"citation":{"ista":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, .","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.","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.","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."},"status":"public","date_created":"2020-02-26T08:46:40Z","publication":"arXiv:1910.03372","type":"preprint","ec_funded":1,"oa":1,"publication_status":"draft","year":"2019","main_file_link":[{"url":"https://arxiv.org/abs/1910.03372","open_access":"1"}],"day":"08","date_published":"2019-10-08T00:00:00Z","language":[{"iso":"eng"}],"page":"61","related_material":{"record":[{"id":"7790","status":"public","relation":"later_version"},{"status":"public","relation":"dissertation_contains","id":"7514"}]},"oa_version":"Preprint","date_updated":"2023-09-07T13:12:41Z","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","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 $\\beta \\rho \\gtrsim 1$."}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"_id":"7524","project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}],"month":"10","publisher":"ArXiv","scopus_import":1,"author":[{"full_name":"Deuchert, Andreas","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert","orcid":"0000-0003-3146-6746"},{"first_name":"Simon","full_name":"Mayer, Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","last_name":"Mayer"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}]}