Fluctuations of doublet splittings using the annular billiard

Journal Article · Mon Nov 01 04:00:00 EST 2004 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.70.056212· OSTI ID:20636864

Egydio de Carvalho, R; Mijolaro, A P ^[1]

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1. Instituto de Geocie e CieExatas, Universidade Estadual Paulista-UNESP 13500-230 Rio Claro, SP (Brazil)

We study the statistical distribution of quantum energy splittings due to a dynamical tunneling. The system, the annular billiard, has whispering quasimodes due to a discrete symmetry that exists even when chaos is present in the underlying classical dynamics. Symmetric and antisymmetric combinations of these quasimodes correspond to quantum doublet states whose degeneracies decrease as the circles become more eccentric. We construct numerical ensembles composed of splittings for two distinct regimes, one which we call semiclassical for high quantum numbers and high energies where the whispering regions are connected by chaos, and other which we call quantal for low quantum numbers, low energies, and near integrable where dynamical tunneling is not a dominant mechanism. In both cases we observe a variation on the fluctuation amplitudes, but their mean behaviors follow the formula of Leyvraz and Ullmo [J. Phys. A 29, 2529 (1996)]. A description of a three-level collision involving a doublet and a singlet is also provided through a numerical example.

• OSTI ID: 20636864
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 70; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
FLUCTUATIONS
INTEGRAL CALCULUS
NUMERICAL ANALYSIS
QUANTUM NUMBERS
SEMICLASSICAL APPROXIMATION
SYMMETRY
TUNNEL EFFECT