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Localization in general one-dimensional random systems

II. Continuum Schrödinger operators

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Abstract

We discuss two ways of extending the recent ideas of localization from discrete Schrödinger operators (Jacobi matrices) to the continuum case. One case allows us to prove localization in the Goldshade, Molchanov, Pastur model for a larger class of functions than previously. The other method studies the model −Δ+V, whereV is a random constant in each (hyper-) cube. We extend Wegner's result on the Lipschitz nature of the ids to this model.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, 606, Kyoto, Japan

    S. Kotani

  2. Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 91125, Pasadena, CA, USA

    B. Simon

Authors
  1. S. Kotani
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  2. B. Simon
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Communicated by E. Lieb

Dedicated to Walter Thirring on his 60th birthday

Research partially supported by USNSF under Grant DMS-8416049

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Kotani, S., Simon, B. Localization in general one-dimensional random systems. Commun.Math. Phys. 112, 103–119 (1987). https://doi.org/10.1007/BF01217682

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  • DOI: https://doi.org/10.1007/BF01217682

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