  We study the motion of a classical particle interacting with one, two, and
finally an infinite chain of 1D 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.
