Mapping the charge-dyon system into the position-dependent effective mass background via Pauli equation

TL;DR

This paper develops a method to model a charge-dyon quantum system within a position-dependent mass framework using the Pauli equation, providing numerical solutions and effective potentials for the analogous system.

Contribution

It introduces a novel approach to map the charge-dyon system into a PDM background via the Pauli equation, including numerical solutions for the mass distribution and effective potentials.

Findings

Numerical solutions for the mass distribution M(r) were obtained.

Effective potentials for the analogous models were derived.

The mapping of eigenvalues starting from minimal angular momentum was studied.

Abstract

This work aims to reproduce a quantum system composed of a charged spin - $1/2$ fermion interacting with a dyon with an opposite electrical charge (charge-dyon system), utilizing a position-dependent effective mass (PDM) background in the non-relativistic regime via the PDM free Pauli equation. To investigate whether there is a PDM quantum system with the same physics (analogous model) that a charge-dyon system (target system), we resort to the PDM free Pauli equation itself. We proceed with replacing the exact bi-spinor of the target system into this equation, obtaining an uncoupled system of non-linear partial differential equations for the mass distribution $M$. We were able to solve them numerically for $M$ considering a radial dependence only, i.e., $M=M(r)$, fixing $\theta_0$, and considering specific values of $\mu$ and $m$ satisfying a certain condition. We present the solutions graphically, and from them, we determine the respective effective potentials, which actually represent our analogous models. We study the mapping for eigenvalues starting from the minimal value $j = \mu - 1/2$.