Propagation of Quantum Expectations with Husimi Functions
Johannes Keller, Caroline Lasser
Source abstract
We analyze the dynamics of expectation values of quantum observables for the time-dependent 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.
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