Correlations of the local density of states in quasi-one-dimensional wires

TL;DR

This paper calculates the correlation function of the local density of states in disordered quasi-one-dimensional wires, revealing detailed dependence on distance and energy difference, including localization and reentrant behaviors.

Contribution

It provides a full dependence of the two-point correlation function on distance using supersymmetric sigma-model, extending understanding of local density of states correlations.

Findings

Reproduces statistics of a single localized wave function at zero energy difference.

Shows reentrant behavior of correlations at the Mott scale.

Provides explicit dependence of correlation function on distance and energy difference.

Abstract

We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric sigma-model, we obtain the full dependence of the two-point correlation function on the distance between the points. In the limit of zero energy difference, our calculation reproduces the statistics of a single localized wave function. At logarithmically large distances of the order of the Mott scale, we obtain a reentrant behavior similar to that in strictly one-dimensional chains.