A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot

TL;DR

This paper presents a geometric method to confine a neutral Dirac particle using noninertial effects, creating bound states similar to quantum dots, with potential applications in condensed matter physics.

Contribution

It introduces a novel geometric approach to confine a Dirac neutral particle via noninertial effects, mimicking quantum dot confinement in relativistic systems.

Findings

Noninertial effects induce a manifold geometry acting as a confining potential.

Relativistic bound states can be achieved through this geometric confinement.

Potential applications in noninertial effects on condensed matter systems.

Abstract

We discuss a geometric approach to confining a Dirac neutral particle with a permanent magnetic dipole moment interacting with external fields to a hard-wall confining potential in the Minkowski spacetime through noninertial effects. We discuss the behaviour of external fields induced by noninertial effects, and a case where relativistic bound states can be achieved in analogous way to having a Dirac particle confined to a quantum dot. We show that this confinement of a Dirac neutral particle analogous to a quantum dot arises from noninertial effects that give rise to the geometry of the manifold playing the role of a hard-wall confining potential. We also discuss the possible use of this mathematical model in studies of noninertial effects on condensed matter systems described by the Dirac equation.