Dynamical transitions in aperiodically kicked tight-binding models

If a localized quantum state in tight-binding model with structural aperiodicity is subject to noisy evolution, then it generally expected result diffusion and delocalization. In this work, shown that the phase of kicked Aubry-Andr\'e-Harper (AAH) robust effects for long times, provided some kick delivered once every time period. However, if strong perturbations are applied by randomly missing kicks, sharp dynamical transition from ballistic growth at initial times diffusive longer observed. Such transitions seen even translationally invariant models. These related existence flat bands, using 2-band we obtain analytical support these observations. The evolution has mechanism similar random walk. scale which takes place characteristics noise. Remarkably, wavepacket scales noise parameters. Further, sequence modulated 'coin toss', argued correlations crucial observed transitions.