Physics (Internal)

Topological Effects of Quasiperiodic Driving

This event is part of the Preliminary Oral Exam.

Topology can underlie the quantization of observables in both static and driven systems, including quasiperiodically driven systems - those driven by multiple incommensurate periodic tones. We derive a topological classification of a class of quasiperiodically driven systems which we call anomalous localized topological phases (ALTPs). The classification depends only on the sum of the spatial dimension and the number of incommensurate tones, a result we can understand intuitively through a formalism known as the frequency lattice. Furthermore, our classification allows us to identify a phase of one-dimensional two-tone-driven ALTPs which can act as a quantized nonadiabatic energy pump between the two drives. We present explicit models in this phase, with which we verify our predictions numerically.