Scattering approach to Anderson localization
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...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | https://eprints.nottingham.ac.uk/54712/ |
| _version_ | 1848799068814311424 |
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| author | Ossipov, A. |
| author_facet | Ossipov, A. |
| author_sort | Ossipov, A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:29:48Z |
| format | Article |
| id | nottingham-54712 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:29:48Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-547122018-09-13T08:14:51Z https://eprints.nottingham.ac.uk/54712/ Scattering approach to Anderson localization Ossipov, A. 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. American Physical Society 2018-08-17 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/54712/1/scatt_approach_arxiv.pdf Ossipov, A. (2018) Scattering approach to Anderson localization. Physical Review Letters, 121 (7). 076601/1-076601/5. ISSN 1079-7114 Anderson localization Disordered systems Techniques S-matrix method in transport http://dx.doi.org/10.1103/PhysRevLett.121.076601 doi:10.1103/PhysRevLett.121.076601 doi:10.1103/PhysRevLett.121.076601 |
| spellingShingle | Anderson localization Disordered systems Techniques S-matrix method in transport Ossipov, A. Scattering approach to Anderson localization |
| title | Scattering approach to Anderson localization |
| title_full | Scattering approach to Anderson localization |
| title_fullStr | Scattering approach to Anderson localization |
| title_full_unstemmed | Scattering approach to Anderson localization |
| title_short | Scattering approach to Anderson localization |
| title_sort | scattering approach to anderson localization |
| topic | Anderson localization Disordered systems Techniques S-matrix method in transport |
| url | https://eprints.nottingham.ac.uk/54712/ https://eprints.nottingham.ac.uk/54712/ https://eprints.nottingham.ac.uk/54712/ |