Dynamical transitions in aperiodically kicked tight-binding models

Abstract

If a localized quantum state in a tight-binding model with structural aperiodicity is subject to noisy evolution, then it is generally expected to result in diffusion and delocalization. In this work, the effects of strongly aperiodic kick sequences applied to a quasiperiodic and a translationally invariant model is studied. It is shown that the kicked Aubry-André-Harper (AAH) model is naturally robust to noise, provided that the kicks are delivered, on average, once every time period. However, if strong noisy perturbation is applied by randomly missing kicks, a sharp dynamical transition from an initial ballistic growth to a subsequent (asymptotic) diffusive growth phase is observed. Such sharp transitions are also present in translation invariant models, where they are related to the existence of flat bands. In both the models, the time scale at which the sharp transition takes place is related to the characteristics of noise, for which analytical support is presented. Remarkably, the spread of the wave function scales with the noise parameters. Further, using kick sequences modulated by a ‘coin toss,’ it is argued that the correlations in the noise are crucial to the observed sharp transitions.