Competing edge and bulk localisation in non-reciprocal disordered systems

TL;DR

This paper explores how non-reciprocal damping and disorder influence localization phenomena in one-dimensional resonator systems, revealing a competition between edge and bulk localization mechanisms.

Contribution

It introduces a symmetrisation approach to analyze spectral properties and clarifies the interplay between edge and bulk localization using Lyapunov exponents.

Findings

Disorder can prevent edge localization caused by imaginary gauge potentials.

The spectral distribution of large systems is characterized in terms of block properties.

Disorder acts as insulation against the non-Hermitian skin effect.

Abstract

We investigate the competing mechanisms of localisation in one-dimensional block disordered subwavelength resonator systems subject to non-reciprocal damping, induced by an imaginary gauge potential. Using a symmetrisation approach to enable the adaptation of tools from Hermitian systems, we derive the limiting spectral distribution of these systems as the number of blocks goes to infinity and characterise their spectral properties in terms of the spectral properties of their constituent blocks. By employing a transfer matrix approach, we then clarify, in terms of Lyapunov exponents, the competition between the edge localisation due to imaginary gauge potentials and the bulk localisation due to disorder. In particular, we demonstrate how the disorder acts as insulation against the non-Hermitian skin effect, preventing edge localisation for small imaginary gauge potentials.