Hybridization of wave functions in onedimensional localization
Abstract
A quantum particle can be localized in a disordered potential, the effect known as Anderson localization. In such a system, correlations of wave functions at very close energies may be described, due to Mott, in terms of a hybridization of localized states. We revisit this hybridization description and show that it may be used to obtain quantitatively exact expressions for some asymptotic features of correlation functions, if the tails of the wave functions and the hybridization matrix elements are assumed to have lognormal distributions typical for localization effects. Specifically, we consider three types of onedimensional systems: a strictly onedimensional wire and two quasionedimensional wires with unitary and orthogonal symmetries. In each of these models, we consider two types of correlation functions: the correlations of the density of states at close energies and the dynamic response function at low frequencies. For each of those correlation functions, within our method, we calculate three asymptotic features: the behavior at the logarithmically large “Mott length scale,” the lowfrequency limit at length scale between the localization length and the Mott length scale, and the leading correction in frequency to this limit. In the several cases, where exact results are available, our method reproduces them within the precision of the orders in frequency considered.
 Publication:

Physical Review B
 Pub Date:
 January 2012
 DOI:
 10.1103/PhysRevB.85.035109
 arXiv:
 arXiv:1111.0339
 Bibcode:
 2012PhRvB..85c5109I
 Keywords:

 73.20.Fz;
 73.21.Hb;
 73.22.Dj;
 Weak or Anderson localization;
 Quantum wires;
 Single particle states;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 10 pages, 5 figures. Several references added, minor corrections corresponding to the journal version