Effect of Minimal lengths on Electron Magnetism

TL;DR

This paper investigates how a minimal length, arising from generalized commutation relations, affects the magnetic properties and energy levels of electrons in a magnetic field, revealing degeneracy removal and new thermodynamic behaviors.

Contribution

It provides an exact solution for energy eigenvalues and eigenfunctions of electrons with minimal length effects in a magnetic field, highlighting degeneracy lifting of Landau levels.

Findings

Degeneracy of Landau levels is removed by minimal length.

Minimal length alters thermodynamic properties at high temperature.

New magnetic behaviors emerge due to minimal length effects.

Abstract

We study the magnetic properties of electron in a constant magnetic field and confined by a isotropic two dimensional harmonic oscillator on a space where the coordinates and momenta operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions. We prove that the usual degeneracy of Landau levels is removed by the presence of the minimal length in the limits of weak and strong magnetic field.The thermodynamical properties of the system, at high temperature, are also investigated showing a new magnetic behavior in terms of the minimal length.