Scattering approach to Anderson localization

Ossipov, A.

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.

Citation

Ossipov, A. (2018). Scattering approach to Anderson localization. Physical Review Letters, 121(7), doi:10.1103/physrevlett.121.076601. ISSN 0031-9007

• Journal Article Type: Article
• Acceptance Date: Jul 24, 2018
• Online Publication Date: Aug 14, 2018
• Publication Date: Aug 17, 2018
• Deposit Date: Aug 16, 2018
• Publicly Available Date: Aug 16, 2018
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 121
• Issue: 7
• Article Number: 076601
• DOI: https://doi.org/10.1103/physrevlett.121.076601
• Keywords: Anderson localization, Disordered systems, Techniques S-matrix method in transport
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.076601