Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

Hiroyuki Yoshimoto, Susumu Kurihara

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    Abstract

    We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas-Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T-d/2, where T is the temperature and d is the dimension of the system.

    Original languageEnglish
    Pages (from-to)10461-10470
    Number of pages10
    JournalJournal of Physics A: Mathematical and General
    Volume36
    Issue number42
    DOIs
    Publication statusPublished - 2003 Nov 24

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    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

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