# Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data

## Ambrosio Luigi - Figalli Alessio - Friesecke Gero - Giannoulis Johannes - Paul Thierry

accepted
year: 2011
journal: Comm. Pure Appl. Math.
abstract: We prove convergence of the Wigner transforms of solutions to the Schrodinger equation, in a semiclassical limit, to solutions to the Liouville equation. We are able to include in our convergence result rough or singular potentials (with Coulomb repulsive singularities) provided convergence is understood for almost all'' initial data. The rigorous statement involves a suitable extension of the DiPerna-Lions theory to the infinite-dimensional space of probability measure, where both the Wigner and the Liouville dynamics can be read. The paper is a continuation of previous work by Ambrosio, Friesecke and Giannoulis.

The paper is available on the cvgmt preprint server.