Directed chaos in a billiard chain with transversal magnetic field

摘要

In generic Hamiltonian systems with a mixed phase space chaotic transport maybe directed and ballistic rather than diffusive. We investigate one particularmodel showing this behaviour, namely a spatially periodic billiard chain inwhich electrons move under the influence of a perpendicular magnetic field. Weanalyze the phase-space structure and derive an explicit expression for thechaotic transport velocity. Unlike previous studies of directed chaos our modelhas a parameter regime in which the dispersion of an ensemble of chaotictrajectories around its moving center of mass is essentially diffusive. Weexplain how in this limit the deterministic chaos reduces to a biased randomwalk in a billiard with a rough surface. The diffusion constant for thissimplified model is calculated analytically.