One-dimensional Anderson Model: Devil's Staircase of Statistical Anomalies
Duration: 1 hour 1 min 26 secs
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| Description: |
Kravstov, V (Trieste)
Tuesday 11 November 2008, 14:00-15:00 |
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| Created: | 2009-01-05 15:54 | ||
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| Collection: | Mathematics and Physics of Anderson Localization: 50 Years After | ||
| Publisher: | Isaac Newton Institute | ||
| Copyright: | Kravstov, V | ||
| Language: | eng (English) | ||
| Distribution: |
World
(downloadable)
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| Credits: |
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| Explicit content: | No | ||
| Aspect Ratio: | 4:3 | ||
| Screencast: | No | ||
| Bumper: | UCS Default | ||
| Trailer: | UCS Default | ||
| Abstract: | Prof. V. Kravstov's version of a talk made a week previously by V. Yudson (Russian Academy of Sciences) on Thursday 06 November 2008.
V.Yudson's Abstract follows: We consider one-dimensional Anderson model of localization on a lattice focusing attention at the probability distribution of the normalized random eigenfunctions. We derive the general formula for the joint probability distribution of the eigenfunction amplitude and phase in the bulk of a long chain in terms of the generation function which obeys the Fokker-Plank like (transfer-matrix) equation. This equation is shown to have anomalous terms at any energy that corresponds to the rational filling factor f (fraction of the states below this energy). At weak disorder the principle anomaly corresponds to f=1/2. The transfer matrix equation in this case is derived and exactly integrated. arXiv:0806.2118v1 Seminar from the Newton Institute programme: Mathematics and Physics of Anderson localization: 50 Years After. http://www.newton.ac.uk/programmes/MPA/seminars/index.html |
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