Lyapunov stability of charge transport in miniband semiconductor superlattices

We discuss a numerical method for the calculation of the spectrum of Lyapunov exponents for spatially extended systems described by coupled Poisson and continuity equations. This approach was applied to the model of collective charge transport in semiconductor superlattices operating in the miniband transport regime. The method is in very good agreement with analytical results obtained for the steady state. As an illustrative example, we consider the collective electron dynamics in the superlattice subjected to an ac voltage and a tilted magnetic field, and conclusively show that, depending on the field parameters, the dynamics can exhibit periodic, quasiperiodic, or chaotic behavior.