### 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 language | English |
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Pages (from-to) | 10461-10470 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 42 |

DOIs | |

Publication status | Published - 2003 Nov 24 |

### ASJC Scopus subject areas

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

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## Cite this

Yoshimoto, H., & Kurihara, S. (2003). Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap.

*Journal of Physics A: Mathematical and General*,*36*(42), 10461-10470. https://doi.org/10.1088/0305-4470/36/42/004