Symmetry of quantum phase space in a degenerate Hamiltonian system
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- Nizhny Novgorod State University, Nizhny Novogorod, 603600, Russia (Russian Federation)
The structure of the global ''quantum phase space'' is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2{mu} (where {mu} is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior. (c) 2000 American Institute of Physics.
- OSTI ID:
- 20217592
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 10, Issue 3; Other Information: PBD: Sep 2000; ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
Similar Records
Sensitivity at the degenerate points of energy levels in a quantum system with nonintegrable perturbation
External field-induced chaos in classical and quantum Hamiltonian systems