Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit

TL;DR

This paper investigates how phase-space noncommutativity influences quantum properties like quantum beating, information, and decoherence in a 2D noncommutative harmonic oscillator, revealing effects on information measures and symmetry considerations.

Contribution

It provides a detailed analysis of noncommutative effects on quantum properties and explores their relation to thermodynamic limits and symmetry-based decoupling mechanisms.

Findings

Noncommutativity affects quantum beating and decoherence.

Missing information is quantified by quantum entropy and mutual information.

Symmetry considerations suggest possible decoupling of noncommutative effects.

Abstract

In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose components behavior we monitor in time. This procedure allows us to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular questions concerning the thermodynamic limit of some relevant properties are also discussed in order to evidence the effects of noncommutativity. Finally, through an analogy with the Zeeman effect, we identify how some aspects of the axial symmetry of the problem suggest the possibility of decoupling the noncommutative quantum perturbations from unperturbed commutative well-known solutions.