Scar Intensity Statistics in the Position Representation

Details Scar Intensity Statistics in the Position Representation Scar Intensity Statistics in the Position Representation

2005-10-18

arxiv.org/abs/nlin/0510040v1

Phys. Rev. E 72, 066204 (2005)

Nonlinear Sciences

Chaotic Dynamics

To appear in Phys. Rev. E, 10 pages, including 4 figures

Scientific paper

10.1103/PhysRevE.72.066204

We obtain general predictions for the distribution of wave function intensities in position space on the periodic orbits of chaotic ballistic systems. The expressions depend on effective system size N, instability exponent lambda of the periodic orbit, and proximity to a focal point of the orbit. Limiting expressions are obtained that include the asymptotic probability distribution of rare high-intensity events and a perturbative formula valid in the limit of weak scarring. For finite system sizes, a single scaling variable lambda N describes deviations from the semiclassical N -> infinity limit.

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