DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, January 10 Padelford C-36 3:45 PM

Propagation of singularities in many-body scattering

András Vasy (MIT)

In this talk I extend the familiar example that singularities of solutions of the wave equation propagate along (generalized) broken bicharacteristics, to many-body scattering. This establishes a connection between the classical and quantum systems. Unlike in the absence of bound states, when quantum propagation is described by classical motion along (broken) bicharacteristics, in the general setting there is a mixing of quantum (bound states) and classical effects even at the level of propagation of singularities. In particular, the characteristic set of the Hamiltonian must be modified to describe the bound states properly. I also explain the implication of these results for the structure of the wave front relation of the scattering matrices, and, time permitting, the relationship of these results to the proof of asymptotic completeness. I will emphasize the geometric structure of the problem, and also briefly mention related geometric phenomena.