Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1998-09-11
Annals of Physics 264, p. 171 (1998)
Nonlinear Sciences
Chaotic Dynamics
20 pages, 11 figures
Scientific paper
10.1006/aphy.1997.5773
The theory of scarring of eigenfunctions of classically chaotic systems by short periodic orbits is extended in several ways. The influence of short-time linear recurrences on correlations and fluctuations at long times is emphasized. We include the contribution to scarring of nonlinear recurrences associated with homoclinic orbits, and treat the different scenarios of random and nonrandom long-time recurrences. The importance of the local classical structure around the periodic orbit is emphasized, and it is shown for an optimal choice of test basis in phase space, scars must persist in the semiclassical limit. The crucial role of symmetry is also discussed, which together with the nonlinear recurrences gives a much improved account of the actual strength of scars for given classical orbits and in individual wavefunctions. Quantitative measures of scarring are provided and comparisons are made with numerical data.
Heller Eric J.
Kaplan Leah
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