The APDE seminar on Monday, 11/21, will be given by Alexis Drouot (U Washington) online (via Zoom) from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (firstname.lastname@example.org).
Title: Dirac operators and topological insulators.
Abstract: I will discuss a 2×2 semiclassical Dirac equation that
emerges from the effective analysis of topological insulators, and
specifically focus on the evolution of coherent states initially
localized on the crossing set of the eigenvalues of the symbol.
Standard propagation of singularities results do not apply; instead,
we discover a surprising phenomenon. The dynamics breaks down in two
parts, one that immediately collapses, and one that propagates along a
seemingly novel quantum trajectory. This observation is consistent
with the bulk-edge correspondence, a principle that coarsely describes
features of transport in topological insulators. We illustrate our
result with various numerical simulations.