Local correlations of different eigenfunctions in a disordered wire
Abstract
The correlation of the local density of states <ρ_{ɛ}( r _{1})ρ_{ɛ + ω}( r _{2})> in quasionedimensional disordered wires in a magnetic field is calculated under the assumption that  r _{1}  r _{2} is much smaller than the localization length. This amounts to finding the zero mode of the transfermatrix Hamiltonian for the supersymmetric σ model, which is done exactly by mapping to the threedimensional 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 quasionedimensional and strictly onedimensional cases are dissimilar.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 March 2007
 DOI:
 10.1134/S0021364007010158
 arXiv:
 arXiv:condmat/0604631
 Bibcode:
 2007JETPL..85...72S
 Keywords:

 73.20.Fz;
 73.21.Hb;
 73.20.Fz;
 73.21.Hb;
 Weak or Anderson localization;
 Quantum wires;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 5 pages, 2 figures. v2: an error in treating the spatial dependence of correlations is corrected