Wigner delay time of a random passive or active medium

We consider the scattering of electrons by a one-dimensional random potential (acting as a passive or active medium) and numerically obtain the probability distribution of the Wigner delay time $\left(\tau \right)$. 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 the 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.