Local correlations of different eigenfunctions in a disordered wire

TL;DR

This paper analyzes local density of states correlations in disordered quasi-one-dimensional wires, revealing how eigenfunction correlations differ between quasi-one-dimensional and strictly one-dimensional systems, using an exact supersymmetric sigma-model approach.

Contribution

It provides an exact calculation of the local density of states correlator in disordered wires, mapping the problem to a Coulomb system to explore different regimes.

Findings

Correlations depend on the distance |r_1 - r_2|, showing level repulsion and attraction regimes.

Eigenfunction correlations differ significantly between quasi-one-dimensional and strictly one-dimensional wires.

Abstract

We calculate the correlator of the local density of states <\rho_{E}(r_1)\rho_{E+\omega}(r_2)> in quasi-one-dimensional disordered wires in a magnetic field, assuming that |r_1-r_2| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric sigma-model, which is done exactly by the mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |r_1-r_2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.