Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving

We derive a topological classification of the steady states of ddimensional lattice models driven by Dincommensurate tones. Mapping to a unifying (d+D-dimensional localized model in frequency space reveals anomalous localized topological phases (ALTPs) with no static analog. While the formal classification is determined by d+D the observable signatures of each ALTP depend on the spatial dimension d For each d with d+D=3 we...