High temperature behavior of a deformed Fermi gas obeying interpolating statistics

TL;DR

This paper explores a q-deformed Fermi gas model to understand interpolating statistics, analyzing its thermodynamic behavior at high temperatures and revealing how deformation parameter q interpolates between bosonic and fermionic behaviors.

Contribution

The study introduces a generalized Fermi-Dirac distribution for q-deformed fermions, demonstrating interpolating statistics and analyzing thermodynamic properties in various dimensions.

Findings

Deformation parameter q interpolates between attractive and repulsive systems.

Model exhibits interpolating statistics in 2D and 3D within 0<q<1.

Third virial coefficient analysis supports the interpolation between bosons and fermions.

Abstract

An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable effectively us to study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high temperature behavior of the system by analyzing the effects of q-deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.