Abstract
Compact billiards in phase space, or action billiards, are defined by truncating the classical Hamiltonian in the action variables. The corresponding quantum mechanical system has a finite Hamiltonian matrix. In this paper we define the compact analogue of common billiards, i.e. straight motion in phase space followed by specular reflections at the boundaries. Computation of their quantum energy spectra establishes that their properties are exactly those of regular billiards: the short range statistics follow the known universality classes depending on the regular or chaotic nature of the motion, whereas the long range fluctuations are determined by the periodic orbits.
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