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

We study the distribution function $P(ω)$ of the random variable $ω= τ_1/(τ_1 + ... + τ_N)$, where $τ_k$'s are the partial Wigner delay times for chaotic scattering in a disordered system with $N$ independent, statistically equivalent channels. In this case, $τ_k$'s are i.i.d. random variables with a distribution $Ψ(τ)$ characterized by a "fat" power-law intermediate tail $\sim 1/τ^{1 + μ}$, truncated by an exponential (or a log-normal) function of $τ$. For $N = 2$ and N=3, we observe a surprisingly rich behavior of $P(ω)$ 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.

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