Resonances in one-dimensional Disordered Chain

TL;DR

This paper investigates the average density of resonances in a semi-infinite disordered chain coupled to a perfect lead, focusing on strong disorder and the asymptotic behavior for small resonance widths.

Contribution

It derives the asymptotic behavior of the average resonance density in a disordered chain under strong disorder conditions.

Findings

Derived the asymptotic form of <ρ(x,y)> for small y

Analyzed resonance behavior in strongly disordered systems

Provided insights into resonance distributions in disordered chains

Abstract

We study the average density of resonances, $<\rho(x,y)>$, in a semi-infinite disordered chain coupled to a perfect lead. The function $<\rho(x,y)>$ is defined in the complex energy plane and the distance $y$ from the real axes determines the resonance width. We concentrate on strong disorder and derive the asymptotic behavior of $<\rho(x,y)>$ in the limit of small $y$.