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Events for September 20, 2018 from General and Seminar calendars

IAMCS Event - Workshop on Quantum Computation and Information

Location: Rudder 701

, Institute for Applied Mathematics and Computational Science
Description: Event Link

The Foias Lectures

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Peter Markowich, KAUST

Title: Propagation of Monokinetic Phase Space Measures with Rough Momentum Profiles

Abstract: Consider a Radon measure which is a phase space probability density carried by the graph of a Lipschitz continuous (or even less regular) vector field. We study the structure of the push-forward of such a measure by a Hamiltonian flow. In particular, we provide an estimate on the number of folds in the support of the transported measure. We also study in detail the type of singularities in the projection of the transported measure in configuration space (averaging out the momentum variable). We analyze the conditions under which this projected measure can have atoms, and give an example in which the projected measure is singular with respect to the Lebesgue measure and diffuse. We discuss applications of our results to the classical limit of the Schrödinger equation. Finally we present various examples and counterexamples showing that our results are sharp.