Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition

TL;DR

This paper provides a comprehensive numerical analysis of the scattering and transport properties of the PBRM model at criticality across the three classical Wigner-Dyson ensembles, confirming multifractal behavior and aligning with analytical and heuristic predictions.

Contribution

It offers the first detailed numerical study of scattering and transport in the PBRM model at criticality for all three Wigner-Dyson ensembles, validating theoretical predictions.

Findings

Good agreement with analytical expressions in the metallic regime

Confirmation that scattering and transport probe multifractality at criticality

Results applicable to experimental investigations of disordered systems

Abstract

An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a good agreement with existing analytical expressions in the metallic regime and with heuristic relations widely used in studies of the PBRM model in the presence of orthogonal and unitary symmetries. Moreover, our results confirm that the multifractal behavior of disordered systems at criticality can be probed by measuring scattering and transport properties, which is of paramount importance from the experimental point of view. Thus, a full picture of the scattering and transport properties of the PBRM model at criticality corresponding to the three classical Wigner-Dyson ensembles is provided.