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 $N\to \infty$ limit.

• Received 17 August 2005

DOI:https://doi.org/10.1103/PhysRevE.72.066204