Wave function intensity statistics from unstable periodic orbits

We examine the effect of short unstable periodic orbits on wave function statistics in a classically chaotic system, and find that the tail of the wave function intensity distribution in phase space is dominated by scarring associated with the least unstable periodic orbits. In an ensemble average over systems with classical orbits of different instabilities, a power-law tail is found, in sharp contrast to the exponential prediction of random matrix theory. The calculations are compared with numerical data, and quantitative agreement is obtained.