Scattering approach to Anderson localization

Ossipov, A. (2018) Scattering approach to Anderson localization. Physical Review Letters, 121 (7). 076601/1-076601/5. ISSN 1079-7114

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Abstract

We develop a novel approach to the Anderson localization problem in a d-dimensional disordered sample of dimension L×Md−1. Attaching a perfect lead with the cross section Md−1 to one side of the sample, we derive evolution equations for the scattering matrix and the Wigner-Smith time delay matrix as a function of L. Using them one obtains the Fokker-Planck equation for the distribution of the proper delay times and the evolution equation for their density at weak disorder. The latter can be mapped onto a nonlinear partial differential equation of the Burgers type, for which a complete analytical solution for arbitrary L is constructed. Analyzing the solution for a cubic sample with M=L in the limit L→∞, we find that for d2 to the metallic fixed point, and provide explicit results for the density of the delay times in these two limits.

Item Type: Article
Keywords: Anderson localization, Disordered systems, Techniques S-matrix method in transport
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1103/PhysRevLett.121.076601
Depositing User: Eprints, Support
Date Deposited: 13 Sep 2018 08:09
Last Modified: 13 Sep 2018 08:14
URI: http://eprints.nottingham.ac.uk/id/eprint/54712

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