Exact results for the Wigner transform phase space densities of a two-dimensional harmonically confined charged quantum gas subjected to a magnetic field

TL;DR

This paper derives exact analytical expressions for the Wigner transform and phase space densities of a two-dimensional harmonically trapped charged quantum gas in a magnetic field, covering various temperature regimes and magnetic strengths.

Contribution

It provides the first exact closed-form solutions for the Wigner transform and phase space densities of this quantum system under arbitrary magnetic fields and temperatures.

Findings

Exact expressions for Wigner transform and phase space densities at various conditions.

Analytic autocorrelation function for the quantum gas.

Approximate densities in the strong magnetic field limit.

Abstract

Closed form analytical expressions are obtained for the Wigner transform of the Bloch density matrix and for the Wigner phase space density of a two dimensional harmonically trapped charged quantum gas in a uniform magnetic field of arbitrary strength, at zero and nonzero temperatures. An exact analytic expression is also obtained for the autocorrelation function. The strong magnetic field case, where only few Landau levels are occupied, is also examined, and useful approximate expressions for the spatial and momentum densities are given.