Quantum to classical correspondence for the Fermi-acceleration model

Abstract

A quantum particle which is confined to the interior of a box with infinitely high but periodically oscillating walls can have an unusual semiclassical limit: For the special case of a one-dimensional linear wall motion we show that the semiclassical domain corresponds to a classical motion in phase space where the initial momentum depends on the particle's position in the box. Another result is that quantum states which correspond to classical cycle-1 fixed points have maximum stability against the boundary induced perturbation (caused by the moving wall). Higher cycle- n fixed points are calculated by numerical bookkeeping up to n = 20. The classical motion is marginally stable. We show how a slight change in the boundary condition will lead to chaotic motion.