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VOLUME 85 (2007) | ISSUE 1 | PAGE 79
Local correlations of different eigenfunctions in a disordered wire
We calculate the correlator of the local density of states \langle \rho_{\varepsilon}(\mathbf{r}_1)
\rho_{\varepsilon + \omega}(\mathbf{r}_2) \rangle in quasi-one-dimensional disordered wires in a magnetic field, assuming that |\mathbf{r}_1 -
\mathbf{r}_2| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric σ model, which is done exactly by mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |\mathbf{r}_1 - \mathbf{r}_2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.