A. VOROS: Stochastic behaviour in classical and quantum Hamiltonian systems

Abstract

(ricevuto 1'8 Aprile 1980) The energy spectrum of a quantum system possessing an integrable classical limit can be conveniently approximated by means of semi-classical quantization rules (i-5). In recent years the problem of finding similar rules for nonintegrable systems has attracted considerable interest (e.9). This particular problem fits naturally into the more general question as to what properties of a quantum system, if any, should be assumed as a counterpart of classical ergodic properties (io-i4). It is now generally agreed that in the discrete-energy spectrum a ((regular)) and an ((irregular ~) part should be distinguished. The former is suitably described by semi-classical quantization in the region of phase-space filled with invariant tori (15.1e).