中国物理B ›› 2009, Vol. 18 ›› Issue (12): 5189-5195.doi: 10.1088/1674-1056/18/12/015

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Finite-size effects in a D-dimensional ideal Fermi gas

苏国珍1, 陈金灿1, 欧聪杰2, Wang A Qiu-Ping2   

  1. (1)Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China; (2)Institut Supérieur des Matériaux et Mécaniques Avancées du Mans, 44 Av. Bartholdi, 72000 Le Mans, France
  • 收稿日期:2009-01-22 修回日期:2009-03-17 出版日期:2009-12-20 发布日期:2009-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10875100).

Finite-size effects in a D-dimensional ideal Fermi gas

Su Guo-Zhen(苏国珍)a)†, Ou Cong-Jie(欧聪杰)b), Wang A Qiu-Pingb), and Chen Jin-Can(陈金灿)a)   

  1. a Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China; b Institut Supérieur des Matériaux et Mécaniques Avancées du Mans, 44 Av. Bartholdi, 72000 Le Mans, France
  • Received:2009-01-22 Revised:2009-03-17 Online:2009-12-20 Published:2009-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10875100).

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摘要： By using the Euler--MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a d-dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.

Abstract: By using the Euler--MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.

Key words: finite-size effect, ideal Fermi gas, thermodynamic property

中图分类号:  (Fermion systems and electron gas)

  • 05.30.Fk
05.70.-a (Thermodynamics)