Bloch oscillations in an aperiodic one-dimensional potential

We study the dynamics of an electron subjected to a static uniform electric field within a one-dimensional tight-binding model with a slowly varying aperiodic potential. The unbiased model is known to support phases of localized and extended one-electron states separated by two mobility edges. We show that the electric field promotes sustained Bloch oscillations of an initial Gaussian wave packet whose amplitude reflects the bandwidth of extended states. The frequency of these oscillations exhibits unique features, such as a sensitivity to the initial wave packet position and a multimode structure for weak fields, originating from the characteristics of the underlying aperiodic potential.