--- res: bibo_abstract: - "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 = \x1F. This result supplements similar recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform imperfect\r\nrepulsive Bose and attractive Fermi gases.@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Krzysztof foaf_name: Mysliwy, Krzysztof foaf_surname: Mysliwy foaf_workInfoHomepage: http://www.librecat.org/personId=316457FC-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Marek foaf_name: Napiórkowski, Marek foaf_surname: Napiórkowski bibo_doi: 10.1088/1742-5468/ab190d bibo_issue: '6' bibo_volume: 2019 dct_date: 2019^xs_gYear dct_identifier: - UT:000471650100001 dct_isPartOf: - http://id.crossref.org/issn/1742-5468 dct_language: eng dct_publisher: IOP Publishing@ dct_title: Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps@ ...