Two-dimensional pauli equation in noncommutative phase-space

TL;DR

This paper explores the effects of noncommutative phase-space on the two-dimensional Pauli equation, deriving energy spectra, wave functions, and thermodynamic properties by mapping to the Landau problem.

Contribution

It introduces a method to analyze the noncommutative Pauli equation using Bopp-shift transformation and examines thermodynamic properties in noncommutative phase-space.

Findings

Energy spectrum and wave functions are obtained for the noncommutative system.

Thermodynamic properties are significantly affected by phase-space noncommutativity.

The noncommutative and commutative cases are compared to highlight differences.

Abstract

In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. We mapped the noncommutative problem to the equivalent commutative one through a set of two-dimensional Bopp-shift transformation. The energy spectrum and the wave function of the two-dimensional noncommutative Pauli equation are found, where the problem in question has been mapped to the Landau problem. Further, within the classical limit, we have derived the noncommutative semi-classical partition function of the two-dimensional Pauli system of one-particle and N-particle systems. Consequently, we have studied its thermodynamic properties, i.e. the Helmholtz free energy, mean energy, specific heat and entropy in noncommutative and commutative phase-spaces. The impact of the phase-space noncommutativity on the Pauli system is successfully examined.