Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors

TL;DR

This paper investigates how phase-space noncommutativity affects quantum mechanics and thermodynamics of free particles and rotors, revealing novel quantization properties, mutual information effects, and deviations from standard quantum results.

Contribution

It introduces new quantization features in noncommutative quantum mechanics and extends the analysis to thermodynamics and quantum rotors in multiple dimensions.

Findings

Noncommutativity induces a Zeeman-like effect in energy spectra.

Mutual information is affected by noncommutative parameters.

Thermodynamic variables show signatures of phase-space noncommutativity.

Abstract

Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of a Zeeman-like effect, the momentum space NC parameter introduces mutual information properties quantified by the quantum purity related to the relevant coordinates of the corresponding Hilbert space. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.