Chaos in a well : Effects of competing length scales

A discontinuous generalization of the standard map, which arises naturally as the dynamics of a periodically kicked particle in a one dimensional infinite square well potential, is examined. Existence of competing length scales, namely the width of the well and the wavelength of the external field, introduce novel dynamical behaviour. Deterministic chaos induced diffusion is observed for weak field strengths as the length scales do not match. This is related to an abrupt breakdown of rotationally invariant curves and in particular KAM tori. An approximate stability theory is derived wherein the usual standard map is a point of ``bifurcation’'.