Ideal Bose and Fermi Gases

Kelly R. Patton, Michael R. Geller, M. P. Blencowe

Marian Apostol

A recently established equivalence between the ideal Bose and Fermi gases [M. H. Lee, Phys. Rev. E 55, 1518 (1997)] is further analyzed with emphasis on the dimensionality effects. The equivalence is shown to be a peculiarity of the bosonlike correlations in two dimensions.

Ravinder Rupchand Puri

Brian P. Cowan

Abstract Knowledge of the chemical potential is essential in application of the Fermi–Dirac and the Bose–Einstein distribution functions for the calculation of properties of quantum gases. We give expressions for the chemical potential of ideal Fermi and Bose gases in 1, 2 and 3 dimensions in terms of inverse polylogarithm functions. We provide Mathematica functions for these chemical potentials together with low- and high-temperature series expansions. In the 3d Bose case we give also expansions about $$T_{{{{\mathrm {B}}}}}$$ T B . The Mathematica routines for the series allow calculation to arbitrary order.

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.