Lorentz symmetry violation and an Analog of Landau levels

TL;DR

This paper explores how Lorentz symmetry violation affects Landau level analogs in a neutral particle system, revealing modified energy spectra and cyclotron dynamics due to Lorentz-breaking vectors.

Contribution

It introduces a nonrelativistic Hamiltonian for a neutral particle in Lorentz-violating electrodynamics and derives the resulting energy spectrum for different Lorentz-breaking vectors.

Findings

Degenerated energy spectrum for time-like and space-like Lorentz-breaking vectors

Energy dependence of cyclotron rotation direction analyzed via supersymmetric quantum mechanics

Modified Landau level analogs due to Lorentz symmetry violation

Abstract

Within the context of Lorentz violating extended electrodynamics, we study an analog of Landau quantization for a system where a neutral particle moves in the presence of an electromagnetic field and a constant four-vector that breaks Lorentz symmetry. The nonrelativistic Hamiltonian associated to this system is obtained using the Foldy-Wouthuysen transformation for a Dirac spinor. The degenerated energy spectrum is obtained for a time-like and a space-like parameter Lorentz-breaking vector. The energy dependence of the cyclotron rotation direction in terms of supersymmetric quantum mechanics is analyzed.