Local correlations of different eigenfunctions in a disordered wire

Details Local correlations of different eigenfunctions in a disordered wire Local correlations of different eigenfunctions in a disordered wire

2006-04-27

arxiv.org/abs/cond-mat/0604631v2

Pis'ma v ZhETF 85, 79 (2007) [JETP Lett. 85, 72 (2007)]

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 2 figures. v2: an error in treating the spatial dependence of correlations is corrected

Scientific paper

10.1134/S0021364007010158

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.

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