Statistics of Resonances in a One-Dimensional Chain: a Weak Disorder Limit

TL;DR

This paper analyzes the statistical properties of resonances in a one-dimensional disordered chain with weak disorder, providing new analytical results that match numerical simulations.

Contribution

It derives novel analytical statistical results for resonance energies in long disordered chains under weak disorder conditions.

Findings

Analytical formulas for resonance statistics in long chains

Good agreement between theory and numerical simulations

Insights into resonance behavior in weakly disordered systems

Abstract

We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main focus of the present study is to describe statistics of the scattered complex energies. We derive compact analytic statistical results for long chains. A comparison of these results has been found to be in good agreement with numerical simulations.