The semiclassical limit of chaotic eigenfunctions

Abstract

A generic chaotic eigenfunction has a non-universal contribution consisting of scars of short periodic orbits. This contribution, which can not be explained in terms of random universal waves, survives the semiclassical limit (when $\hslash$ goes to zero). In this limit, the sum of scarred intensities is a simple function of $\eta \equiv \sqrt{\pi /2}(f-1)h_T^{-1}(\sum {\lambda }_i^2{)}^{1/2}$, with $f$ the degrees of freedom, $h_T$ the topological entropy and $\{{\lambda }_i\}$ the set of positive Lyapunov exponents. Moreover, the fluctuations of this representation go to zero as $1/|\ln \hslash |$. For this reasson, we will be able to provide a detailed description of a generic chaotic eigenfunction in the semiclassical limit.

4 pages, 1 poscript figure