Floquet Media - a dynamic and spectral approach

Over the last few decades, there has been a rapid growth in the study of periodic materials in condensed matter physics, cold atoms, photonics, and elastics. Floquet media are periodic materials on which time-periodic forcing is applied to effectively alter their properties; for example, transforming a conductor into an insulator by shining light on it. The ability to change the energy transport properties of a material by acting on it externally has the potential to revolutionize energy storage, data transmission and processing devices, and quantum computing technology, among other things.

Mathematically, however, much is still unknown, and much of the existing theory is based on simplified models whose validity is limited only to particular physical regimes. We propose to study Floquet media through first-principle continuum models. Such infinite-dimensional dynamical systems are known to be rich in phenomena and require a broad set of techniques.

Our proposed research will answer three fundamental questions: First, how does energy transport in an infinite crystal changes under forcing. Second, is it possible to trap energy near the edge of the crystal when forced, or is energy destined to radiate away. Third, is the classical description of wave packets breakup from non-driven systems extend to Floquet media.