Scattering for Schrodinger operators with conical decay
Abstract: In this talk, I will discuss the scattering properties of Schrodinger operators with potentials that have short-range decay along a collection of rays in . This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along all rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece that may interact with the potential for a long time. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial.
I will state our results, sketch some of the main ideas in the proof, and briefly discuss some examples of these interacting states for different systems. This is joint work with Adam Black.
