Alex Watson

Wave-packet dynamics in locally periodic media

We study the dynamics of wave-packet solutions of Schr\”{o}dinger’s equation and Maxwell’s equations in media with a local periodic structure which varies adiabatically (over many periods of the periodic lattice) across the medium. We focus in particular on the case where symmetries of the periodic structure lead to degeneracies in the Bloch band dispersion surface. We derive systematically and rigorously the `anomalous velocity’ of wave-packets due to the Bloch band’s Berry curvature, and the dynamics of a wave-packet incident on a Bloch band degeneracy in one spatial dimension. Joint work with Michael Weinstein and Jianfeng Lu.