Скачать или смотреть Joint Quantum Classical Hamilton Variation Principle in the Phase Space by Dmitry Zhdanov

Title: Joint Quantum Classical Hamilton Variation Principle in the Phase Space
Presenter: Dmitry Zhdanov, Institute of Spectroscopy of the Russian Academy of Sciences, Moscow, Russia
Conference: Koopman Methods in Classical and Classical-Quantum Mechanics
Sponsored by: Wilhelm und Else Heraeus-Stiftung and Tulane University
Conference Website Link: https://bit.ly/2Vchwri

At first glance, the Hamilton variation principle cannot be formulated for quantum particles since they lack well-defined trajectories. I will show how to overcome this seemingly formidable obstacle using Husimi representation of quantum mechanics based on our recent result.
The dynamics of a closed quantum system in Husimi representation can be treated as a flow of multidimensional probability fluid in the phase space. By introducing the classical counterpart of Husimi representation in close analogy to Koopman-von Neumann theory, one can largely unify the formulations of classical and quantum dynamics.
I will prove that the motions of elementary parcels of both classical and
quantum Husimi fluid obey Hamilton variation principle, and the differences between associated action functionals stem from the differences between classical and quantum pure states.
Husimi action functionals are not unique and defined up to the Skodje flux gauge fixing. The gauge choice can dramatically alter flux trajectories. For instance, I will show that the Bohmian mechanics is nothing but the Husimi representation in a different gauge. I will also briefly outline an application of the presented formalism for improving semiclassical initial value representations employed in quantum many-body simulations.