Semiclassical limit of chaotic eigenfunctions

A generic chaotic eigenfunction has a non-universal contribution consisting of scars of short periodic orbits. This contribution, which cannot be predicted by a model of random universal waves, survives the semiclassical limit (when ℎ goes to zero). In this limit, the sum of scarred intensities only depends on η ≡ (f - 1)(Σλ2i)1/2/hT, with f the degrees of freedom, {λi} the set of positive Lyapunov exponents and hT the topological entropy. Moreover, taking into account that relative fluctuations of the scarred intensities tend to zero as 1/|ln ℎ|, we are able to provide a detailed description of a generic chaotic eigenfunction in the semiclassical limit. Our conclusions were verified in the Bunimovich stadium billiard