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Manifestations of classical phase space structures in quantum mechanics

1993; Elsevier BV; Volume: 223; Issue: 2 Linguagem: Inglês

10.1016/0370-1573(93)90109-q

1873-6270

O. Bohigas, Steven Tomsovic, Denis Ullmo,

Nonlinear Photonic Systems

Using two coupled quartic oscillators for illustration, the quantum mechanics of simple systems whose classical analogs have varying degrees of non-integrability is investigated. By taking advantage of discrete symmetries and dynamical quasidegeneracies it is shown that Percival's semiclassical classification scheme, i.e., eigenstates may be separated into a regular and an irregular group, basically works. This allows us to probe deeply into the workings of semiclassical quantization in mixed phase space systems. Some observations of intermediate status states are made. The standard modeling of quantum fluctuation properties exhibited by the irregular states and levels by random matrix ensembles is then put on a physical footing. Generalized ensembles are constructed incorporating such classical information as fluxes crossing partial barriers and relative fractions of phase space volume occupied by interesting subregions. The ensembles apply equally well to both spectral and eigenstate properties. They typically show non-universal, but nevertheless characteristic level fluctuations. In addition, they predict “semiclassical localization” of eigenfunctions and “quantum suppression of chaos” which are quantitatively borne out in the quantum systems.