Quantum Spectra and Wave Functions in Terms of Periodic Orbits for Weakly Chaotic Systems

Details Quantum Spectra and Wave Functions in Terms of Periodic Orbits for Weakly Chaotic Systems Quantum Spectra and Wave Functions in Terms of Periodic Orbits for Weakly Chaotic Systems

2000-09-30

arxiv.org/abs/nlin/0010001v1

Physica Scripta T90, 134 (2001).

Nonlinear Sciences

Chaotic Dynamics

9 pages, 8 eps figures

Scientific paper

10.1238/Physica.Topical.090a0013

Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and manifesting possible chaotic behavior. Such phase space regions are characterized as being close to periodic orbits of an integrable reference system. The states are often rather striking, and can be concentrated in spatial regions. This leads to possible phenomena. We review some methods we have introduced to characterize such regions and find analytic formulas for the special states and their energies.

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