## Topological classes of quantum dynamics in quasi-periodically driven systems

**Speaker:**Phil Crowley, Boston University

**When:**October 9, 2019 (Wed), 03:30PM to 04:30PM (add to my calendar)

**Location:**SCI 328

*This event is part of the Condensed Matter Theory Seminar Series. *

Advances in the control and manipulation of experimental quantum systems has allowed us to realise new driven phases of quantum matter in the laboratory. In periodically driven systems new phases occur when the steady states, determined by Bloch-Floquet theorem, have novel spatio-temporal or topological order.

In this talk I show how the Bloch-Floquet theorem is generalised to cases when the drives are not periodic, but rather quasi-periodic.

I apply this framework to the simplest case of a few level system, and show that steady state dynamics admit a topological classification. When the classification is non-trivial the system exhibits a quantised pumping of energy, and a sensitivity to initial conditions, neither of which is present in the trivial case.

I further discuss the stability of this classification, the behaviour near the critical point where the topological class changes, and ongoing work to observe this in experiments.