Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states

TL;DR

This paper investigates the quantum behavior of electrons in a noncommutative 2D space under electromagnetic influence, focusing on Landau levels, thermodynamics, and constructing specialized coherent states.

Contribution

It introduces matrix and quaternionic vector coherent states for a noncommutative space, advancing the understanding of quantum states in such geometries.

Findings

Construction of matrix vector coherent states (MVCS)

Development of quaternionic vector coherent states (QVCS)

Analysis of thermodynamic properties in noncommutative space

Abstract

The behavior of an electron in an external uniform electromagnetic background coupled to a harmonic potential, with noncommuting space coordinates, is considered in this work. The thermodynamics of the system is studied. Matrix vector coherent states (MVCS) as well as quaternionic vector coherent states (QVCS), satisfying required properties, are also constructed and discussed.