# MPA

## Seminar

### One-dimensional Anderson model: devil's staircase of statistical anomalies

#### Abstract

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#### Video

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