Understanding the Random Displacement Model: From Ground-State Properties to Localization

Details Understanding the Random Displacement Model: From Ground-State Properties to Localization Understanding the Random Displacement Model: From Ground-State Properties to Localization

2011-07-02

arxiv.org/abs/1107.0386v2

Physics

Mathematical Physics

31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 2010

Scientific paper

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.

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