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arXiv · 1107.0386

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

Frédéric Klopp·Michael Loss·Shu Nakamura·Günter Stolz
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Abstract

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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Frédéric Klopp, Michael Loss, Shu Nakamura, Günter Stolz. 2011-07-02. Understanding the Random Displacement Model: From Ground-State Properties to Localization. https://arxiv.org/abs/1107.0386

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