UBC Math Department Colloquium: Amir Sagiv

The last decade has witnessed tremendous experimental progress in the study of "Floquet media", crystalline materials whose properties are altered by time-periodic parametric forcing. Theoretical advancements, however, have so far been achieved through discrete and approximate models. Understanding these materials from their underlying, first-principle PDE models, however, remains an open problem.

A key question is that of Floquet Edge Modes - wave-packets that propagate along the edge of the materials and do not disperse into the bulk. It is not known whether such modes exist in PDE models. We study a model of a material with a domain wall, and rigorously show that the propagation of physically relevant wave-packets is governed by a Dirac equation. This dynamical-systems approach allows us to show, both numerically and analytically, that localized edge-modes decay due to a resonance phenomenon.