Structural invariance and the energy spectrum

DOI10.1088/0305-4470/32/39/303zbMATH Open0946.81027arXivchao-dyn/9902009OpenAlexW3102809972MaRDI QIDQ4947805

R. A. Mendez, F. Leyvraz, Thomas H. Seligman

Publication date: 25 April 2000

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the semiclassical limit, is extended to the energy spectra of bounded time independent systems. We proceed by showing that the results obtained previously for the quasi-energies and eigenphases of the S-matrix can be extended to the eigenphases of the quantum Poincare map which is unitary in the semiclassical limit. We then show that its eigenphases in the chaotic case move rather stiffly around the unit circle and thus their local statistical fluctuations transfer to the energy spectrum via Bogomolny's prescription. We verify our results by studying numerically the properties of the eigenphases of the quantum Poincare map for billiards by using the boundary integral method.

Full work available at URL: https://arxiv.org/abs/chao-dyn/9902009

zbMATH Keywords

quantum chaos structural invariance bounded time-independent systems eigenphases of the quantum Poincaré map

Mathematics Subject Classification ID

Quantum chaos (81Q50) Quantum equilibrium statistical mechanics (general) (82B10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)