Department of

# Mathematics

Seminar Calendar
for Harmonic Analysis and Differential Equations events the year of Friday, October 22, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, November 2, 2021

1:00 pm in 347 Altgeld Hall,Tuesday, November 2, 2021

#### Floquet Hamiltonians - effective gaps and resonant decay

###### Amir Sagiv   [email] (Columbia U, Applied Math)

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 an optical waveguides array, we see how such modes decay and disappear due to resonant coupling with the radiation modes.