Propagation of Quantum Expectations with Husimi Functions

Abstract

We analyze the dynamics of expectation values of quantum observables for the time-dependent semiclassical Schrodinger equation. To benefit from the positivity of Husimi functions, we switch between observables obtained from Weyl and anti-Wick quantization. We develop and prove a second order Egorov-type propagation theorem with Husimi functions by establishing transition and commutator rules for Weyl and anti-Wick operators. We provide a discretized version of our theorem and present numerical experiments for Schrodinger equations in dimensions two and six that validate our results.