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The semiclassical limit of chaotic eigenfunctions

Eduardo G. Vergini
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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 $\hbar$ goes to zero). In this limit, the sum of scarred intensities is a simple function of $η\equiv \sqrt{π/2} (f-1) h^{-1}_T (\sum λ_i^2)^{1/2} $, with $f$ the degrees of freedom, $h_T$ the topological entropy and $\{λ_i\}$ 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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Eduardo G. Vergini. 2002-04-30. The semiclassical limit of chaotic eigenfunctions. https://arxiv.org/abs/nlin/0205001

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