Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

TL;DR

This paper investigates how the classical limit of quantum oscillators on a noncommutative space affects phase-space localization, revealing non-commuting limits related to noncommutativity parameters.

Contribution

It analyzes the non-commuting classical limits of quantum oscillators on noncommutative spaces through phase-space localization of Wigner functions.

Findings

Limits of noncommutative parameters do not commute in the classical limit.

Phase-space localization properties differ depending on the order of limits.

Wigner functions of coherent states reveal the non-commutative effects.

Abstract

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.