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

Abstract

We study the distribution function P(ω) of the random variable ω = τ1/(τ1 +· · ·+τN), where τk ’s are the partial Wigner delay times for chaotic scattering in a disordered system with N independent, statistically equivalent channels. In this case, τk’s are independent and identically distributed random variables with a distribution (τ ) characterized by a “fat” power-law intermediate tail ∼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.