Statistical properties of phases and delay times of the one-dimensional Anderson model with one open channel

We study the distribution of phases and of Wigner delay times for a one-dimensional Anderson model with one open channel. Our approach, based on classical Hamiltonian maps, allows us an analytical treatment. We find that the distribution of phases depends drastically on the parameter σA=σ/sink where σ² is the variance of the disorder distribution and k the wave vector. It undergoes a transition from uniformity to singular behavior as σA increases. The distribution of delay times shows universal power-law tails 1/τ², while the short time behavior is σA dependent.