Thursday, April 13, 2023
Time  Items 

All day 

4:00pm 
04/13/2023  4:00pm We study Schrodinger equations which are periodic in space and time. These models are inspired by recent experimental progress in the study of wave propagation and quantum mechanics under timeperiodic forcing. Timeperiodic Hamiltonians, however, are not as well understood as their static (autonomous) analogs. In particular, many discrete models of periodic materials (e.g., of graphene) are known to develop spectral gaps under a timeperiodic driving. In PDEs, however, no such gaps are conjectured to form. How do we reconcile these two facts? Using periodic homogenization, we prove that the driven Schrodinger equation has an “effective gap”  a new and physicallyrelevant relaxation of a spectral gap. Taking a broader perspective, we ask  how does timeperiodic forcing affect a general band structure? We will show that a spectrallylocal notion of stability can be formulated and proved, in a way which again corresponds with periodic homogenization theory. Location:
LOM 205
