Thermodynamic Properties of a Quantum Group Boson Gas $GL_{p,q}(2)$

TL;DR

This paper introduces a method using quantum group $GL_{p,q}(2)$ to analyze the thermodynamic properties of a bosonic system, revealing how deformation parameters influence physical quantities and connecting to known results in the limit.

Contribution

It develops a novel approach employing quantum group formalism to study bosonic thermodynamics, extending traditional models with deformation parameters $p$ and $q$.

Findings

Average number of particles depends on $p$ and $q$

Pressure calculations incorporate deformation parameters

Results reduce to classical case when $p=q=1$

Abstract

An approach is proposed enabling to effectively describe the behaviour of a bosonic system. The approach uses the quantum group $GL_{p,q}(2)$ formalism. In effect, considering a bosonic Hamiltonian in terms of the $GL_{p,q}(2)$ generators, it is shown that its thermodynamic properties are connected to deformation parameters $p$ and $q$. For instance, the average number of particles and the pressure have been computed. If $p$ is fixed to be the same value for $q$, our approach coincides perfectly with some results developed recently in this subject. The ordinary results, of the present system, can be found when we take the limit $p=q=1$.