Abstract:

Velocity averaging in classical kinetic models [1,2,3] like Vlasov or Boltzmann equation is a smoothing
mechanism for „macroscopic“ observables (in position space) as averages in the velocity variable of the phase space distribution function.
The Wignertransform [4,5,6,7] converts the Schrödinger (or von Neumann) equation into sort of Vlasov equation for the Wignerfunction, with the standard transport term and a nonlocal (i.e. pseudodifferential) force term. It is a long standing question if one can apply velocity averaging to quantum kinetic Wigner equations, in order to obtain a gain of regularity on quantities such as the density function.
In this talk we introduce kinetic equations and the classical averaging lemma and then show that this indeed works also in the quantum physics case, for special mixed states, but typically fails for pure states (similar to the situation for the global in time semiclassical limit of nonlinear Schrödinger equations [5,6]).
We use a new (?) derivation of Madelung's fluid dynamic formulation of Schrödinger equations [8].
Joint work with Jakob Möller.

Zoom-Link:
us06web.zoom.us/j/81595699552