Thermodynamic equivalence of certain ideal Bose and Fermi gases

Kelly R. Patton, Michael R. Geller and Miles P. Blencowe

Physica A: Statistical Mechanics and its Applications, 2005, vol. 357, issue 3, 427-435

Abstract: It has been established recently that there is an interesting thermodynamic “equivalence” between noninteracting Bose and spinless Fermi gases in two dimensions, and between one-dimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble. These are known to be special cases of a larger class of equivalences of noninteracting systems having an energy-independent single-particle density of states (DOS). Furthermore, the thermodynamic equivalence has also been established for any noninteracting quantum gas with a discrete ladder-type spectrum in the canonical ensemble. Here we investigate the intriguing possibility that the equivalence for systems with a constant DOS is a special case of a more general equivalence between noninteracting Bose and Fermi gases with a discrete ladder-type spectrum in the grand-canonical ensemble, which reduces to the constant-DOS case when the level-spacing approaches zero. By direct numerical calculation of the Bose and Fermi grand-canonical free energies, we conclude that the grand-canonical equivalence does not apply to the ladder-spectrum case.

Keywords: Ideal Bose gas; Ideal Fermi gas (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:357:y:2005:i:3:p:427-435

DOI: 10.1016/j.physa.2005.03.039

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