Distribution of S-matrix poles for one-dimensional disordered wires

TL;DR

This paper investigates how the distribution of S-matrix poles in one-dimensional disordered wires depends on disorder type and coupling strength, revealing super-radiance transitions and effects of correlations.

Contribution

It introduces an effective non-Hermitian Hamiltonian approach to analyze S-matrix poles in 1D disordered wires with correlated and uncorrelated disorder.

Findings

Identification of pole distribution patterns as a function of disorder and coupling

Observation of super-radiance transition at perfect coupling

Effects of disorder correlations on pole distribution

Abstract

By the use of the effective non-Hermitian Hamiltonian approach to scattering we study the distribution of the scattering matrix (S-matrix) poles in one-dimensional (1D) models with various types of diagonal disorder. We consider the case of 1D tight-binding wires, with both on-site uncorrelated and correlated disorder, coupled to the continuum through leads attached to the wire edges. In particular, we focus on the location of the S-matrix poles in the complex plane as a function of the coupling strength and the disorder strength. Specific interest is paid to the super-radiance transition emerging at the perfect coupling between wire and leads. We also study the effects of correlations intentionally imposed to the wire disorder.