Wave chaos in quantum systems with point interaction

Journal Article · Mon Jul 01 04:00:00 EDT 1991 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01057882· OSTI ID:5368956

Albeverio, S ^[1]; Seba, P ^[2]

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1. Ruhr Univ. Bochum (West Germany) CERFIM, Locarno (Switzerland)
2. Ruhr Univ. Bochum (West Germany) Univ. of Essen (West Germany)

The authors study perturbations {cflx H} of the quantized version {cflx H}{sub 0} of integrable Hamiltonian systems by point interactions. They relate the eigenvalues of {cflx H} to the zeros of a certain meromorphic function {xi}. Assuming the eigenvalues of {cflx H}{sub 0} are Poisson distributed, they get detailed information on the joint distribution of the zeros of {xi} and give bounds on the probability density for the spacings of eigenvalues of {cflx H}. Their results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.

• OSTI ID: 5368956
• Journal Information: Journal of Statistical Physics; (United States), Journal Name: Journal of Statistical Physics; (United States) Vol. 64:1-2; ISSN 0022-4715; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
QUANTUM MECHANICS
QUANTUM OPERATORS
STOCHASTIC PROCESSES
WAVE EQUATIONS