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arXiv:hep-th/9610124 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Anyonic behavior of quantum group gases

Marcelo R. Ubriaco

Published Jan 1, 1997• 75 citations
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Abstract

We first introduce and discuss the formalism of ${\mathrm{SU}}_{\mathrm{q}}$ (N) bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for N=2. We show that quantum group gases exhibit anyonic behavior in D=2 and 3 spatial dimensions. In particular, for a ${\mathrm{SU}}_{\mathrm{q}}$ (2) boson gas at D=2 the parameter q interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.

DOI
10.1103/physreve.55.291

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A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose–Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range [Formula: see text]. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.