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Closed form analytical expressions are obtained for the Wigner transform ofthe Bloch density matrix and for the Wigner phase space density of a twodimensional harmonically trapped charged quantum gas in a uniform magneticfield of arbitrary strength, at zero and nonzero temperatures. An exactanalytic expression is also obtained for the autocorrelation function. Thestrong magnetic field case, where only few Landau levels are occupied, is alsoexamined, and useful approximate expressions for the spatial and momentumdensities are given.

physics letters a

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