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Spectral Analysis of Quantum Hamiltonians pp 183–219Cite as

Birkhäuser

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

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 224))

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 Schrödinger 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.

Mathematics Subject Classification (2010). 82B44 (primary), 47B80 (secondary).

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Author information

Authors and Affiliations

  1. IMJ, UMR CNRS 7586 Université Pierre et Marie Curie, Case 186 4 place Jussieu, F-75252, Paris cedex 05, France

    Frédéric Klopp

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332-0160, USA

    Michael Loss

  3. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokya, Japan, 153-8914

    Shu Nakamura

  4. Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama, 35294-1170, USA

    Günter Stolz

Authors
  1. Frédéric Klopp
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  2. Michael Loss
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  3. Shu Nakamura
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  4. Günter Stolz
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Corresponding author

Correspondence to Frédéric Klopp .

Editor information

Editors and Affiliations

  1. , Departamento de Física, P. Universidad Católica de Chile, Santiago, 22, Chile

    Rafael Benguria

  2. , Departamento de Matemáticas, Universidad de Chile, Las Palmeras, Nuñoa 3425, Santiago, Chile

    Eduardo Friedman

  3. , Departamento de Matemática, Universidad de Chile, Las Palmeras, Nuñoa 3425, Santiago, Chile

    Marius Mantoiu

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Klopp, F., Loss, M., Nakamura, S., Stolz, G. (2012). Understanding the Random Displacement Model: From Ground State Properties to Localization. In: Benguria, R., Friedman, E., Mantoiu, M. (eds) Spectral Analysis of Quantum Hamiltonians. Operator Theory: Advances and Applications, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0414-1_10

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