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Modern Physics Letters B

IMPLICATIONS OF INTERPOLATIVE QUANTUM STATISTICS — A REVIEW

R. RAMANATHAN

Published Feb 20, 1995• 2 citations
Publisher

Abstract

A review of the interpolative quantum statistics is presented. It is shown, by imposing a positivity condition on the distribution function, that this statistics subsumes Gentile's intermediate statistics and is far richer than Gentile's statistics, apart from being a genuine quantum statistics. It is also capable of accounting for the possible very small violations of statistics in physical processes. It is finally pointed out that this statistics offers an elegant and useful parametrization of Haldane's 'statistical interaction', while retaining all the interesting features of the latter. Some of the statistical mechanics that these distribution functions lead to are also examined.

DOI
10.1142/s0217984995000140

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A review of the interpolative quantum statistics is presented. It is shown, by imposing a positivity condition on the distribution function, that this statistics subsumes Gentile's intermediate statistics and is far richer than Gentile's statistics, apart from being a genuine quantum statistics. It is also capable of accounting for the possible very small violations of statistics in physical processes. It is finally pointed out that this statistics offers an elegant and useful parametrization of Haldane's 'statistical interaction', while retaining all the interesting features of the latter. Some of the statistical mechanics that these distribution functions lead to are also examined.
We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution function interpolates continuously between the Fermi-Dirac and the Bose-Einstein limits. We present an explicit solution of the transcendental equation for the didtribution function in a general case, as well as determine the thermodynamic properties in both low- and high-temperature limits.