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

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

2011-09-06

arxiv.org/abs/1109.1279v1

Phys. Rev. E 84, 035203(R) (2011)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevE.84.035203

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.

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