Universality of the Wigner Time Delay Distribution for One-Dimensional Random Potentials

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out on samples whose sizes are large compared to the localization length (localized regime). The case of small samples is also discussed (ballistic regime). We provide a physical argument which explains in a quantitative way the origin of the exponential divergence of the moments. The occurrence of a log-normal tail for finite size systems is analyzed. Finally, we present exact results in the low energy limit which clearly show a departure from the universal behavior.