Dynamical Transitions in Aperiodically Kicked Tight Binding Models

Generally, upon the introduction of noise, coherence in a quantum system is quickly lost and the dynamics of a localised state becomes diffusive. However, we have found that the Aubry-André-Harper model, a tight-binding model with kicked, quasiperiodic on-site disorder is robust to the effects of noise in the periodicity and amplitude of the kick. Moreover, under a protocol which delivers kicks at random intervals, we have been able to engineer a sharp, dynamical, ballistic-to-diffusive transition, with the break time decided by the characteristics of the noise. Such behaviour even takes place for translationally invariant systems. Considering a 2-band model, we have found that this behaviour is related to the existence of flat bands, and the mechanism for asymptotic diffusion is similar to that of a classical random walk.