Exact theory for the quantum eigenstates of a strongly chaotic system. (English) Zbl 0727.70028
Consider the classical system of a point particle free to move on a compact Riemannian surface of constant negative curvature. This system exhibits a strongly chaotic behaviour under suitable circumstances. The authors give an exact description of the corresponding quantum eigenstates of this system. The main result relates suitably smoothed sums over the quantum wave function to a kind of classical orbit length spectrum.
Reviewer: S.I.Andersson (Göteborg)
MSC:
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 58Z05 | Applications of global analysis to the sciences |
| 81Q50 | Quantum chaos |
Keywords:
classical system of a point particle; compact Riemannian surface of constant negative curvature; strongly chaotic behaviour; quantum wave function; classical orbit length spectrumReferences:
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