Thermodynamics Properties of Confined Particles on Noncommutative Plane

TL;DR

This paper investigates the thermodynamic behavior of particles confined on a noncommutative plane, analyzing effects like internal energy, heat capacity, and Bose-Einstein condensation, with focus on the noncommutative parameter's influence.

Contribution

It introduces a detailed thermodynamic analysis of particles on a noncommutative plane, including effective magnetization and Bose-Einstein condensation, which are novel in this context.

Findings

Corrections to internal energy and heat capacity due to noncommutativity

Effective magnetization and susceptibility depend on the noncommutative parameter

Conditions for Bose-Einstein condensation in the noncommutative setting

Abstract

We consider a system of $N$ particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding internal energy and heat capacity where different corrections are obtained. In analogy with the magnetic field case, we define an effective magnetization and study its susceptibility in terms of the noncommutative parameter $\theta$. By introducing the chemical potential, we investigate the Bose-Einstein condensation for the present system. Different limiting cases related to the temperature and $\theta$ will be analyzed as well as some numerical illustration will be presented.