Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems

TL;DR

This paper investigates how quantum eigenfunctions in disordered metallic grains exhibit long-range correlations and fluctuations in their inverse participation ratio moments, influenced by conductance and grain geometry, using diffusion spectrum analysis.

Contribution

It introduces a detailed analysis of eigenfunction fluctuations in finite disordered systems at finite conductance, linking them to the diffusion spectrum and extending beyond universal random matrix predictions.

Findings

Eigenfunction moments fluctuate at finite conductance.

Fluctuation distributions depend on grain geometry.

Long-range correlations affect eigenfunction statistics.

Abstract

This paper is devoted to the statistics of the quantum eigenfunctions in an ensemble of finite disordered systems (metallic grains). We focus on moments of inverse participation ratio. In the universal random matrix limit that corresponds to the infinite conductance of the grains, these moments are self-averaging quantities. At large but finite conductance the moments do fluctuate due to the long range correlations in the eigenfunctions. We evaluate the distributions of fluctuations at given conductance and geometry of the grains and express them through the spectrum of the diffusion operator in the grain.