Symmetry breaking between statistically equivalent, independent channels in a few-channel chaotic scattering

Abstract

We study the distribution function $P(\omega )$ of the random variable $\omega ={\tau }_1/({\tau }_1+...+{\tau }_N)$, where ${\tau }_k$'s are the partial Wigner delay times for chaotic scattering in a disordered system with $N$ independent, statistically equivalent channels. In this case, ${\tau }_k$'s are i.i.d. random variables with a distribution $\Psi (\tau )$ characterized by a "fat" power-law intermediate tail $\sim 1/{\tau }^{1+\mu }$, truncated by an exponential (or a log-normal) function of $\tau$. For $N=2$ and N=3, we observe a surprisingly rich behavior of $P(\omega )$ revealing a breakdown of the symmetry between identical independent channels. For N=2, numerical simulations of the quasi one-dimensional Anderson model confirm our findings.

4 pages, 5 figures

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