Events
DMS Applied and Computational Mathematics Seminar |
| Time: Nov 07, 2025 (02:00 PM) |
| Location: 328 Parker Hall |
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Details:  Speaker: Amir Sagiv (New Jersey Institute of Technology (NJIT))
Title: Floquet Hamiltonians - Spectrum and Dynamics
Abstract: The last couple of decades witnessed tremendous experimental progress in the study of "Floquet media," crystalline materials whose properties are changed by applying a time-periodic parametric forcing. The theory of Floquet media has so far been restricted to discrete models, which are often heuristic and approximate. Understanding these materials from their underlying PDE models, such as the Schrödinger equation, remains an open problem.
Specifically, semi-metals such as graphene are known to transform into "Floquet Insulators" under such periodic driving. While traditionally this phenomenon is modeled by a spectral gap, in PDE models no such gaps are conjectured to form. How do we reconcile these seemingly contradictory statements? We prove the existence of an “effective gap” – a novel and physically-relevant notion which generalizes a (proper) spectral gap. Adopting a broader perspective, we will then survey newer results on dispersion and spectral near-invariance in bulk Floquet materials.
Host: Junshan Lin
ACM seminar’s website: https://sites.google.com/view/yzhangpaul/applied-and-computational-mathematics-seminars
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