{"abstract":[{"lang":"eng","text":"We discuss thermodynamic properties of harmonically trapped\r\nimperfect quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition of the mean-field interparticle potential energy as compared\r\nto the homogeneous case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments that this model corresponds to the limiting case of\r\na long-ranged interparticle potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation similar to the well-known Kac scaling\r\nprocedure, which is presented here in a form adapted to the case of an isotropic\r\nharmonic trap. We show that within the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein condensation provided d > 1.\r\nThe main result of our analysis is that in d = 1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill\r\nthe relation aB + aF = \u001f. This result supplements similar recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform imperfect\r\nrepulsive Bose and attractive Fermi gases."}],"article_number":"063101","language":[{"iso":"eng"}],"date_updated":"2023-08-29T07:19:13Z","author":[{"last_name":"Mysliwy","id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof","full_name":"Mysliwy, Krzysztof"},{"last_name":"Napiórkowski","first_name":"Marek","full_name":"Napiórkowski, Marek"}],"publisher":"IOP Publishing","scopus_import":"1","intvolume":"      2019","department":[{"_id":"RoSe"}],"_id":"6840","doi":"10.1088/1742-5468/ab190d","date_created":"2019-09-01T22:00:59Z","publication":"Journal of Statistical Mechanics: Theory and Experiment","external_id":{"arxiv":["1810.02209"],"isi":["000471650100001"]},"citation":{"mla":"Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:<a href=\"https://doi.org/10.1088/1742-5468/ab190d\">10.1088/1742-5468/ab190d</a>.","ista":"Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063101.","ieee":"K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019.","apa":"Mysliwy, K., &#38; Napiórkowski, M. (2019). Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/ab190d\">https://doi.org/10.1088/1742-5468/ab190d</a>","short":"K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019).","ama":"Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2019;2019(6). doi:<a href=\"https://doi.org/10.1088/1742-5468/ab190d\">10.1088/1742-5468/ab190d</a>","chicago":"Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2019. <a href=\"https://doi.org/10.1088/1742-5468/ab190d\">https://doi.org/10.1088/1742-5468/ab190d</a>."},"status":"public","day":"13","quality_controlled":"1","oa":1,"ec_funded":1,"publication_status":"published","year":"2019","title":"Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps","publication_identifier":{"eissn":["1742-5468"]},"article_processing_charge":"No","oa_version":"Preprint","volume":2019,"project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"month":"06","issue":"6","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"journal_article","isi":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.02209"}],"date_published":"2019-06-13T00:00:00Z"}