Resonance width distribution for high-dimensional random media

TL;DR

This paper investigates how the distribution of resonance widths in 3D random media reveals different regimes like metallic, localized, and critical, providing a new criterion for the metal-insulator transition verified through numerical simulations.

Contribution

It introduces a novel analysis of resonance width distributions to identify system regimes and proposes a new criterion for the metal-insulator transition in 3D disordered systems.

Findings

Resonance width distribution distinguishes different regimes in 3D media.

Identifies system-inherent fingerprints for metallic, localized, and critical phases.

Proposes a new criterion for the metal-insulator transition.

Abstract

We study the distribution of resonance widths P(G) for three-dimensional (3D) random scattering media and analyze how it changes as a function of the randomness strength. We are able to identify in P(G) the system-inherent fingerprints of the metallic, localized, and critical regimes. Based on the properties of resonance widths, we also suggest a new criterion for determining and analyzing the metal-insulator transition. Our theoretical predictions are verified numerically for the prototypical 3D tight-binding Anderson model.