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-dim ensional Anderson model with one open channel. Our approach, based on class ical Hamiltonian maps, allows us an analytical treatment. We find that the distribution of phases depends drastically on the parameter sigma(A) = sigm a/sin k where sigma(2) is the variance of the disorder distribution and k t he wave vector. It undergoes a transition from uniformity to singular behav ior as sigma(A) increases. The distribution of delay times shows universal power-law tails l/tau(2), while the short time behavior is sigma(A) depende nt.