Nonlinear dynamics and band transport in a superlattice driven by a plane wave

A quantum particle transport induced in a spatially-periodic potential by a propagating plane wave has a number important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices and cold atoms in optical crystal. Here we apply kinetic description of the directed transport in a superlattice beyond standard linear approximation, and utilize exact path-integral solutions of the semiclassical transport equation. We show that the particle drift and average velocities have non-monotonic dependence on the wave amplitude with several prominent extrema. Such nontrivial kinetic behaviour is related to global bifurcations developing with an increase of the wave amplitude. They cause dramatic transformations of the system phase space and lead to changes of the transport regime. We describe different types of phase trajectories contributing to the directed transport and analyse their spectral content.