Open Problems in Periodically Driven Systems
This event is part of the PhD Final Oral Exams.
Examining Committee: Anatoli Polkovnikov, Emanuel Katz, Claudio Chamon, Shyam Erramilli and Pankaj Mehta
I will present some open problems in the study of periodically driven (Floquet) closed quantum systems. I will ﬁrst introduce the inverse-frequency expansion as a time-dependent Schrieﬀer-Wolﬀ transformation for Floquet systems, and then discuss ideas about the regimes of validity and its convergence properties. I will demonstrate how the latter depend severely on the rotating frame chosen. After that, I will present an energy-space many-body localised model which does not absorb energy from the drive all the way up to and including inﬁnite times, but for which the inverse-frequency expansion nevertheless diverges. As a follow up I will clarify the relation between the convergence of the expansion and heating in globally-driven many-body systems. If time permits, further open problems will be presented.