Abstract
We discuss a quantum version of the Fermi acceleration model, which consists of a particle bouncing between a fixed and oscillating wall. The actual movement of the particle crucially depends on the boundary conditions of the Schrödinger equation. Under Dirichlet boundary conditions, the quantum system displays a regular behaviour, but its classical limit exhibits some unphysical attributes. Only for certain initial conditions does it correspond to the stable motion of a ball bouncing once for an integer number of wall oscillations. In the classical model that situation gives rise to regular islands imbedded in the chaotic sea.
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Karner, G. On the quantum Fermi accelerator and its relevance to ‘quantum chaos’. Lett Math Phys 17, 329–339 (1989). https://doi.org/10.1007/BF00399758
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DOI: https://doi.org/10.1007/BF00399758