On the distribution of the Wigner time delay in one-dimensional disordered systems

TL;DR

This paper derives the probability distribution of Wigner time delay in one-dimensional disordered systems, showing it aligns with random matrix theory predictions and is described by an exponential functional of the potential.

Contribution

It provides a unified distribution for Wigner time delay across different models and links it to a stochastic process involving exponential functionals.

Findings

Distribution matches predictions from random matrix theory.

The stochastic process is characterized as an exponential functional of the potential.

Distribution is consistent across different models.

Abstract

We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.