Propagation of Quantum Expectations with Husimi Functions

• Autores: Johannes Keller, Caroline Lasser
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 4, 2013, págs. 1557-1581
• Idioma: inglés
• DOI: 10.1137/120889186
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• Resumen

  • 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