Thermodynamic equivalence of certain ideal Bose and Fermi gases

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish
Pages (from-to)427-435
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Volume357
Issue number3-4
DOIs
StatePublished - Nov 15 2005

Keywords

  • Ideal Bose gas
  • Ideal Fermi gas

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