Wehrl entropies and Euclidean Landau levels

TL;DR

This paper investigates Wehrl entropies associated with Euclidean Landau levels, deriving explicit formulas for thermal states of the harmonic oscillator and analyzing their properties and temperature dependence.

Contribution

It provides explicit expressions for Wehrl entropies at Euclidean Landau levels and explores their properties and temperature behavior, linking phase-space measures to quantum Landau levels.

Findings

Explicit Wehrl entropy formulas for Landau levels.

Analysis of Wehrl entropy behavior with temperature.

Connection between Husimi functions and Laguerre distributions.

Abstract

We are concerned with an information-theoretic measure of uncertainty for quantum systems. Precisely, the Wehrl entropy of the phase-space probability $Q^{(m)}_{\hat{\rho}}=\left\langle z,m|\hat{\rho}|z,m\right\rangle $ which is known as Husimi function, where $\hat{\rho}$ is a density operator and $% \left|z,m\right\rangle $ are coherent states attached to an Euclidean $m$th Landau level. We obtain the Husimi function $Q^{(m)}_{\beta}$ of the thermal density operator $\hat{\rho}_{\beta}$ of the harmonic oscillator, which leads by duality, to the Laguerre probability distribution of the mixed light. We discuss some basic properties of $Q^{(m)}_{\beta}$ such as its characteristic function and its limiting logarithmic moment generating function from which we derive the rate function of the sequence of probability distributions $Q^{(m)}_{\beta},\ m=0,1,2,...$. For $m\geq1$, we establish an exact expression for the Wehrl entropy of the density operator $% \hat{\rho}_{\beta}$ and we discuss the behavior of this entropy with respect to the temperature parameter $T=1/\beta$