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 language | English |
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Pages (from-to) | 427-435 |
Number of pages | 9 |
Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 357 |
Issue number | 3-4 |
DOIs | |
State | Published - Nov 15 2005 |
Keywords
- Ideal Bose gas
- Ideal Fermi gas