Quantum flow on the phase space

Abstract

In this project, we will survey the quantum and semiclassical dynamics of wave packets on the grounds of the phase space's vector flow. Up to date this flow had been studied for the Wigner function and we want to start a similar study for the Husimi distribution of quantum states, the last based on a description involving a basis of coherent states. This work will be realized with two approaches. In the first, we regard the phase space as a rigid structure where the wave packet's dynamic is developed under a continuity equation, analogous to the Schrödinger equation; and we are interested in the relations between the quantum and classical flows, because they can serve as markers of quantum phenomena. In the second approach, the phase space is built as a dynamical structure with properties inherited from its classical counterpart, thus being a good background for semiclassical analysis. (AU)