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An Introduction to the Mathematics of Anderson Localization

Author: GŁnter Stolz
Url: http://arxiv.org/abs/1104.2317
Format: Ps, Pdf
Year: 2011
Category: Mathematical Physics
Pages: 38
Clicks: 1617

We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss spectral as well as dynamical localization and provide proofs based on the fractional moments (or Aizenman-Molchanov) method. We also discuss, in less self-contained form, the extension of the fractional moment method to the continuum Anderson model. Finally, we mention major open problems. These notes are based on several lecture series which the author gave at the Kochi School on Random Schr\"odinger Operators,

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