Propagation of quantum expectations with husimi functions

We analyze the dynamics of expectation values of quantum observables for the timedependent semiclassical Schrödinger 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 Schrödinger equations in dimensions two and six that validate our results.