Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model

TL;DR

This paper investigates the disorder-induced localization transition in a 3D network model of a class C superconductor, using a novel mapping to classical random walks to achieve precise numerical analysis of critical behavior.

Contribution

It introduces a new approach linking quantum localization phenomena to classical random walks, enabling more accurate numerical studies of the Anderson transition in class C systems.

Findings

Identifies critical behavior at the Anderson transition in the model.

Establishes a connection between conductance, density of states, and classical random walks.

Provides more precise numerical results than previous studies.

Abstract

We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behaviour at an Anderson transition than has been possible previously in any context.