Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory

TL;DR

This paper reviews recent advances in understanding quantum scattering in mesoscopic systems with complex geometries, focusing on non-universal features like delay times and resonance widths that go beyond traditional Random Matrix Theory predictions.

Contribution

It highlights the importance of non-perturbative methods to incorporate system-specific features in the analysis of quantum scattering, extending beyond universal RMT results.

Findings

Distribution of Wigner delay times reflects non-universal system characteristics.

Resonance widths are linked to scattering matrix poles and system geometry.

Non-perturbative approaches are essential for accurate modeling of complex quantum systems.

Abstract

We review recent developments on quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogs shows diffusive, localized or critical behavior are considered. These are features that cannot be described by the universal Random Matrix Theory results. Instead one has to go beyond this approximation and incorporate them in a non-perturbative way. Here, we pay particular emphasis to the traces of these non-universal characteristics, in the distribution of the Wigner delay times and resonance widths. The former quantity captures time dependent aspects of quantum scattering while the latter is associated with the poles of the scattering matrix.