Chaotic classical scattering and dynamics in oscillating 1-D potential wells

We study the motion of a classical particle interacting with one, two, and finally an infinite chain of 1-D square wells with oscillating depth. For a single well we find complicated scattering behavior even though there is no topological chaos due to the absence of hyperbolic periodic orbits. In contrast, for two coupled square wells there is chaotic scattering. The infinite oscillating chain yields the generic transition to chaos, with diffusion in energy and in space, as the separation between wells is increased. We briefly discuss the relevance of our results to solid state physics.