On the classical dynamics of charged particle in special class of spatially non-uniform magnetic field

TL;DR

This paper investigates the classical dynamics of a charged particle in a specific class of non-uniform magnetic fields, providing integral solutions and analyzing supersymmetry breaking in exponentially decaying fields.

Contribution

It introduces a general integral equation for certain non-uniform magnetic fields and explores supersymmetry properties in these fields, extending classical analysis beyond uniform cases.

Findings

Derived integral equations for specific non-uniform magnetic fields

Provided solutions for particular magnetic field configurations

Showed supersymmetry breaking in exponentially decaying magnetic fields

Abstract

Motion of a charged particle in uniform magnetic field has been studied in detail, classically as well as quantum mechanically. However, classical dynamics of a charged particle in non-uniform magnetic field is solvable only for some specific cases. We present in this paper, a general integral equation for some specific class of non-uniform magnetic field and its solutions for some of them. We also examine the supersymmetry of Hamiltonians in exponentially decaying magnetic field with radial dependence and conclude that this kind of non-uniformity breaks supersymmetry.