Thermodynamic properties of a charged particle in non-uniform magnetic field

TL;DR

This paper analytically investigates the thermodynamic properties of a charged particle in a non-uniform magnetic field, revealing how magnetic susceptibility and specific heat vary with temperature, magnetic field strength, and non-uniformity.

Contribution

It provides exact solutions for energy spectrum and thermodynamic quantities of a charged particle in a non-uniform magnetic field using the Nikiforov-Uvarov method, including explicit relations for the partition function.

Findings

Specific heat and magnetic susceptibility increase with magnetic field strength at low temperatures.

Thermodynamic quantities decrease at high temperatures due to higher energy level occupation.

Transition from positive to negative magnetic susceptibility depends on the non-uniformity parameter.

Abstract

We solve the Schr\"odinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, $\alpha$, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties. On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.