Title: Directional Ballistic transport for partially periodic Schrödinger operators


Abstract: In this talk, we will consider Schrödinger operators on R^d or Z^d with bounded potentials V that are periodic in some direction and compactly supported in others. Such systems are known to produce "surface states" confined near the potential's support. Specifically, we will focus on the transport properties of these states – in other words, the rate at which these states spread in different directions. Roughly speaking, we say that a state exhibits ballistic motion if it spreads linearly in time
( x~t - in some sense). We show that, under very mild assumptions, a class of surface states exhibits what we describe as directional ballistic transport, consisting of a strong form of ballistic transport in the periodic directions and its absence in the other directions. Furthermore, we show, in some models, that a dense set of surface states exhibit this surface ballistic transport property. In this talk, I will briefly review our main results and some of the tools used in this work. We would also have a brief discussion on the term "ballistic transport" and its uses in different contexts. This is joint work with Adam Black, David Damanik, and Giorgio Young.