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Texas A&M University
Mathematics

Mathematical Physics and Harmonic Analysis Seminar

Date: October 15, 2021

Time: 1:50PM - 2:40PM

Location: BLO306&Zoom

Speaker: Amir Sagiv, Columbia University

  

Title: Floquet Hamiltonians - effective gaps and resonant decay

Abstract: Floquet topological insulators are an emerging category of materials whose properties are transformed by time-periodic forcing. Can their properties be understood from their first-principles continuum models, i.e., from a driven Schrodinger equation? First, we study the transformation of graphene from a conductor into an insulator under a time-periodic magnetic potential. We show that the dynamics of certain wave-packets are governed by a Dirac equation, which has a spectral gap property. This gap is then carried back to the original Schrodinger equation in the form of an “effective gap” - a new and physically-relevant relaxation of a spectral gap. Next, we consider periodic media with a localized defect, and ask whether edge/defect modes remain stable under forcing. In a model of planar waveguides, we see how such modes decay and disappear due to resonant coupling with the radiation modes.