Local correlations of different eigenfunctions in a disordered wire
Abstract
We calculate the correlator of the local density of states <E(r1)E+ω(r2)> in quasi-one-dimensional disordered wires in a magnetic field, assuming that |r1-r2| 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 |r1-r2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.
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