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Physical Review A

Quon gas with the boson, fermion, and near-classical limits

Akira Inomata

Published Aug 1, 1995• 11 citations
Publisher

Abstract

A simple quon gas model which interpolates between the boson gas and the fermion gas is proposed. The fermion limit is realized without use of the exclusion principle. The second and third virial coefficients are calculated and compared with those of a free anyon gas. If the fugacity is small the system can simulate an anyon gas which has the Maxwell-Boltzmann limit.

DOI
10.1103/physreva.52.932

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A simple quon gas model which interpolates between the boson gas and the fermion gas is proposed. The fermion limit is realized without use of the exclusion principle. The second and third virial coefficients are calculated and compared with those of a free anyon gas. If the fugacity is small the system can simulate an anyon gas which has the Maxwell-Boltzmann limit.
Thermodynamical properties of a model quon gas are reported. The quons considered are the objects obeying the deformed commutator aa†−qa†a=1 with −1⩽q⩽1. Although q=1 and q=−1 correspond respectively to boson and fermion statistics, it is not trivial to generate a quon gas which interpolates between the boson gas and the fermion gas without Pauli’s exclusion principle. The proposed model, interpolating between the two limits, can realize the Maxwell-Boltzmann limit at q=0 and simulate a free anyon gas. Under the restriction −1⩽q⩽1, the gas is deformed but bosonic in nature. It shows the Bose-Einstein condensation even in two dimensions.
The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons. The parameter qqq attached to a quon labels a smooth interpolation between bosons ( q=+1q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+1q=+1) and fermions ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$). Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. We generalize this and show that qcomposite=qconstituentn2{q}_{\mathrm{composite}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q}_{\mathrm{constituent}}^{{n}^{2}}qcomposite​=qconstituentn2​ for a system of nnn identical quons. Using this generalization, we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.
For three anyons confined in a harmonic oscillator, only the class of states that interpolates nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full three-body partition function as was done in an earlier publication [J. Law, A. Suzuki, and R. Bhaduri, Phys. Rev. A 46, 4693 (1992)], here only the nonlinear contribution is calculated, thus avoiding delicate cancellations between the irrelevant linear part and the two-body partition function. Our numerical results are consistent with the simple analytical form suggested recently by Myrheim and Olaussen [Phys. Lett. B 299, 267 (1993)].