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Scar intensity statistics in the position representation
1Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA.
Abstract:
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 , instability exponent 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 lambdaN variable describes deviations from the semiclassical N--> infinity limit.
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