Quantum Distributions for the Plane Rotator

TL;DR

This paper develops quantum phase-space distributions for the plane rotator, linking wave functions in angle and angular momentum representations, and explores their classical and quantum properties at finite temperature.

Contribution

It introduces a framework for quantum distributions of the plane rotator using wave functions in dual representations, emphasizing the role of quantization and temperature effects.

Findings

Quantum distributions are defined using wave functions in dual representations.

Quantum superposition relates Fourier dual variables and conjugate coordinates.

Finite temperature wave functions can produce classical sound waves.

Abstract

Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual variable and the canonically conjugate coordinate. The standard quantization condition for angular momentum appears as necessary for consistency. It is shown that at finite temperature the time dependence of the quantum wave functions may provide classical sound waves. Non-thermal quantum entropy is associated with localization along the orbit.