Speaker
Description
Classical phase space dynamics is governed by a continuity equation. The same is true for
quantum dynamics in phase space: Wigner's quantum phase space current, J, governs the
evolution of Wigner's phase space distribution W.
Unlike the classical case, W is typically negative in some regions. These negative regions
represent quantum coherences.
Also, the current's velocity field is ill-defined. It is singular when W = 0. I show that
this implies that there are no trajectories in quantum phase space.
With these velocity singularities Liouvillian phase space volumes feature singular changes
too. I will show that this is necessary in order for quantum dynamics to create
coherences. This is worth knowing particularly for numerical investigations.
Stationary points of J are important for both, classical and quantum dynamics, maybe even
more so in the quantum case, since the dynamics can move and split or merge these
stagnation points. But the existence of stagnation points is constrained by a topological
conservation law which quantum mechanics has to obey (see Figure).
While velocity fields and trajectories are ill-defined in quantum phase space, I show that
the current J is always well behaved. It can be studied, providing new insights, and it
can be numerically integrated to study the dynamics.