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

TL;DR

This paper investigates the distribution of partial delay times in chaotic scattering with multiple channels, revealing symmetry breaking between statistically identical channels, supported by numerical simulations for N=2.

Contribution

It uncovers symmetry breaking phenomena in delay time distributions for multiple channels in chaotic scattering, with detailed analysis for N=2 and N=3, and confirms findings through numerical simulations.

Findings

Distribution P(ω) exhibits symmetry breaking for N=2 and N=3.

Numerical simulations confirm the theoretical predictions for N=2.

Rich behavior of P(ω) indicates complex channel interactions.

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.