Statistics of resonances in one-dimensional disordered systems

TL;DR

This paper reviews and presents new results on the statistical properties of resonances in one-dimensional disordered systems, exploring different models, regimes, and their relation to Wigner delay times.

Contribution

It introduces new findings on resonance statistics in 1D disordered systems and highlights their connection to Wigner delay times across various models and regimes.

Findings

Resonance statistics are linked to Wigner delay times.

New results apply to both continuous and lattice models.

The study covers different disorder strengths and coupling regimes.

Abstract

The paper is devoted to the problem of resonances in one-dimensional disordered systems. Some of the previous results are reviewed and a number of new ones is presented. These results pertain to different models (continuous as well as lattice) and various regimes of disorder and coupling strength. In particular, a close connection between resonances and the Wigner delay time is pointed out and used to obtain information on the resonance statistics.