Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian

Abstract

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.

Transformation of quasi-distributions

“…Also, the mathematically identical formulation was developed in the field of time-frequency analysis with very similar ideas and operator transformations [5][6][7][8][9][10][11][12][13]. For general quantum mechanical considerations see for example [14][15][16][17][18].…”