Symmetry breaking between statistically equivalent, independent channels in 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 independent and identically distributed random variables with a distribution Ψ(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.