High and low temperature behavior of a quantum group fermion gas

TL;DR

This paper investigates the thermodynamic behavior of an $SU_q(2)$ invariant fermionic system, revealing how the deformation parameter $q$ influences entropy, virial coefficients, and fractional statistics in three dimensions.

Contribution

It introduces an analysis of $SU_q(2)$ fermions' thermodynamics, demonstrating the connection between $q$ and fractional statistics in three dimensions.

Findings

Entropy bounds differ for $q>1$ and $q<1$ at low temperatures.

The second virial coefficient's sign depends on $q$ and vanishes at $q=1.96$.

$q$ interpolates between fermionic and bosonic behaviors, indicating fractional statistics.

Abstract

We consider the simplest $SU_{q}(2)$ invariant fermionic hamiltonian and calculate the low and high temperature behavior for the two distinct cases $q>1$ and $q<1$. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to $q\neq 1$. At high temperatures we find that the sign of the second virial coefficient depends on $q$, and vanishes at $q=1.96$. An important consequence of this fact is that the parameter $q$ connects the fermionic and bosonic regions, showing therefore that $SU_{q}(2)$ fermions exhibit fractional statistics in three spatial dimensions.