Universality of the Wigner time delay distribution for one-dimensional random potentials

摘要

We show that the distribution of the time delay for one-dimensional randompotentials is universal in the high energy or weak disorder limit. Ouranalytical results are in excellent agreement with extensive numericalsimulations carried out on samples whose sizes are large compared to thelocalisation length (localised regime). The case of small samples is alsodiscussed (ballistic regime). We provide a physical argument which explains ina quantitative way the origin of the exponential divergence of the moments. Theoccurence of a log-normal tail for finite size systems is analysed. Finally, wepresent exact results in the low energy limit which clearly show a departurefrom the universal behaviour.