# Analysis Seminar

#### On Wigner and Bohmian Measures in Semiclassical Quantum Dynamics

**Speaker:**
Christof Sparber, University of Illinois, Chicago

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, March 26, 2015, 10 a.m.

**Synopsis:**

We report on a series of recent mathematical results in the description of semiclassical quantum dynamics, jointly obtained (in different parts) with: P. Markowich, C. Klein, A. Figalli, and T. Paul. We consider a class of phase-space measures, which naturally arise from the Bohmian interpretation of quantum mechanics. These, so-called, Bohmian measures describe the time-evolution of the quantum mechanical position and velocity densities and are given by the push-forward under the Bohmian flow on phase space. The latter can be seen as a perturbation of the classical Hamiltonian flow. We study the classical limit of this flow and of the associated Bohmian measure, whenever the dimensionless Planck's constant tends to zero. Connections to the, by now, classical theory of Wigner measures are also discussed.