### 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 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*36*(42), 10461-10470. https://doi.org/10.1088/0305-4470/36/42/004

**Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap.** / Yoshimoto, Hiroyuki; Kurihara, Susumu.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 36, no. 42, pp. 10461-10470. https://doi.org/10.1088/0305-4470/36/42/004

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TY - JOUR

T1 - Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

AU - Yoshimoto, Hiroyuki

AU - Kurihara, Susumu

PY - 2003/11/24

Y1 - 2003/11/24

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0242382572&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242382572&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/42/004

DO - 10.1088/0305-4470/36/42/004

M3 - Article

AN - SCOPUS:0242382572

VL - 36

SP - 10461

EP - 10470

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

ER -