Ideal Fermi gases in harmonic oscillator potential traps

Yushan Li

Yi Xue-Xi, Haijun Wang, Chang-Pu Sun

Bose–Einstein Condensation (BEC) of both the ideal and the weakly inter-acting cold alkali gases confined by anisotropic harmonic oscillator poten-tials is investigated in this paper. It is shown that the transition point is shifted towards lower temperatures because of the trapped potentials, and the specific heat below the transition point is no longer proportional to T 3/2 . Expressions of modified condensation temperature, internal energy and the specific heat are derived for the ideal trapped gases explicitly. Moreover, the effect of interactions among the atoms on the transition temperature is also given and discussed.

Yeong E. Kim, Alexander L. Zubarev

David J. Toms

We study the thermodynamic properties of an ideal gas of fermions in a harmonic oscillator confining potential. The analogy between this problem and the de Haas-van Alphen effect is discussed and used to obtain analytical results for the chemical potential and specific heat in the case of both isotropic and anisotropic potentials. Step-like behaviour in the chemical potential, first noted in numerical studies, is obtained analytically and shown to result in an oscillatory behaviour of the specific heat when the particle number is varied. The origin of these oscillations is that part of the thermodynamic potential is responsible for the de Haas-van Alphen-type effect. At low temperatures we show analytically that there are significant deviations in the specific heat from the expected linear temperature dependence, again as a consequence of the de Haas-van Alphen part of the thermodynamic potential. Results are given for one, two, and three spatial dimensions. In the anisotropic case we show how the specific heat jumps as the ratio of oscillator frequencies varies. © 2005 Elsevier Inc. All rights reserved.

Shah Mohammad Bahauddin, Mir Mehedi Faruk

Abstract From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.

W. Wonneberger