Distribution of Wigner delay time from single channel disordered systems

TL;DR

This paper derives an analytical expression for the distribution of Wigner delay times in single-channel disordered systems, demonstrating universality across different types of disorder within a random phase approximation.

Contribution

It provides a universal analytical formula for delay time distribution in one-dimensional disordered systems, confirming previous results and extending understanding of disorder effects.

Findings

Analytical expression for $P_s( au)$ derived

Results agree with previous models, indicating universality

Delay time distribution is independent of disorder type

Abstract

We consider the scattering of an electron from a semi-infinite one-dimensional random medium. The random medium is characterized by force, $-\d V/\d L$ being the basic random variable. We obtain an analytical expression for the stationary delay time ($\tau$) distribution $P_s(\tau)$ within a random phase approximation. Our result agrees with earlier analytical expressions, where the random potential is taken to be of different kind, indicating universality of the delay time distribution, i.e., delay time distribution is independent of the nature of disorder.