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Analytical treatment of interacting Fermi gas in 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 Thomas-Fermi approximation agrees well with exact results for any dimension even though system is dilute and small, i.e. when the Thomas-Fermi approximation is generally expected to fail. In the high temperature (classical) region, we find interaction energy decreases in proportion to T^(-d/2), where T is temperature and d is dimension of the system. Effect of interaction in the ground state in two and three-dimensional systems is also discussed.

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Hiroyuki Yoshimoto, Susumu Kurihara. 2002-10-09. Analytical treatment of interacting Fermi gas in arbitrary dimensional harmonic trap. https://doi.org/10.1088/0305-4470%2F36%2F42%2F004

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