Wigner delay time from a random passive and active medium

TL;DR

This paper investigates the distribution of Wigner delay times in one-dimensional random media, revealing universal long-time tails and the effects of absorption on delay time statistics through numerical simulations.

Contribution

It extends previous analytical results to strong disorder regimes and compares passive and active media, highlighting the universality and suppression of long delay times due to absorption.

Findings

Delay time distribution follows a 1/τ^2 tail in passive media.

Strong disorder causes the tail to persist, indicating universality.

Absorption suppresses the long-time tail exponentially.

Abstract

We consider the scattering of electron by a one-dimensional random potential (both passive and active medium) and numerically obtain the probability distribution of Wigner delay time ($\tau$). We show that in a passive medium our probability distribution agrees with the earlier analytical results based on random phase approximation. We have extended our study to the strong disorder limit, where random phase approximation breaks down. The delay time distribution exhibits the long time tail ($1/\tau^2$) due to resonant states, which is independent of the nature of disorder indicating the universality of the tail of the delay time distribution. In the presence of coherent absorption (active medium) we show that the long time tail is suppressed exponentially due to the fact that the particles whose trajectories traverse long distances in the medium are absorbed and are unlikely to be reflected.