Ballistic transport properties of a 2D rippled mesoscopic channel: Classical regime

We use the classical billiard model to study electronic transport properties of a 2D electronic channel where one boundary is sinusoidal and the other is flat. Computer simulations reveal the essential dependence on the parameters ν = a/b and γ = d/b (a, b and d are, respectively, the amplitude and period of the ripple and the width of the channel). We calculate transmission coefficient, average number of collisions, mean dwelling time, and outgoing distribution of particles for an appropriate initial distribution of 105 particles. Poincare sections show that the dynamics of the individual particles consists of chaotic (deterministic) and regular regions. The contribution of the regular and chaotic orbits to transport is identified. It is also shown that orbits lying on the separatrix and on some other chaotic regions are responsible for the extremely long dwelling times and the fractal structure of certain curves. We compare some of our results with those which consider collisions with random profiles. (author)