A Landau-type quantization from a Lorentz symmetry violation background with crossed electric and magnetic fields

TL;DR

This paper explores a Landau-type quantization effect induced by Lorentz symmetry violation in the presence of crossed electric and magnetic fields, analyzing its spectral properties under various confining potentials.

Contribution

It introduces a novel Landau-like quantization arising from Lorentz symmetry violation and studies its spectral characteristics with different confining potentials.

Findings

Discrete energy spectrum under hard-wall confinement

Cyclotron frequency depends on quantum numbers

Quantum effects emerge from Lorentz symmetry violation

Abstract

We investigate the arising of an analogue of the Landau quantization from a background of the violation of the Lorentz symmetry established by a time-like 4-vector and a field configuration of crossed electric and magnetic field. We also analyse the effects on this Landau-type system subject to a hard-wall confining potential by showing a particular case where a discrete spectrum of energy can be obtained. Further, we analyse the effects of a linear confining potential on the Landau-type system. We show that a quantum effect characterized by the dependence of the cyclotron frequency on the quantum numbers of the system can arise in this analogue of the Landau system. As an example, we calculate the cyclotron frequency associated with ground state of the system.