The semiclassical limit of chaotic eigenfunctions

Details The semiclassical limit of chaotic eigenfunctions The semiclassical limit of chaotic eigenfunctions

2002-04-30

arxiv.org/abs/nlin/0205001v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 1 poscript figure

Scientific paper

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 $\hbar$ goes to zero). In this limit, the sum of scarred intensities is a simple function of $\eta\equiv \sqrt{\pi /2} (f-1) h^{-1}_T (\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 $1/|\ln \hbar|$. For this reasson, we will be able to provide a detailed description of a generic chaotic eigenfunction in the semiclassical limit.

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