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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2011, Issue 660


A continuum version of the Kunz–Souillard approach to localization in one dimension

David Damanik / Günter Stolz
Published Online: 2011-04-14 | DOI: https://doi.org/10.1515/crelle.2011.070


We consider continuum one-dimensional Schrödinger operators with potentials that are given by a sum of a suitable background potential and an Anderson-type potential whose single-site distribution has a continuous and compactly supported density. We prove exponential decay of the expectation of the finite volume correlators, uniform in any compact energy region, and deduce from this dynamical and spectral localization. The proofs implement a continuum analog of the method Kunz and Souillard developed in 1980 to study discrete one-dimensional Schrödinger operators with potentials of the form background plus random.

About the article

Received: 2010-02-08

Revised: 2010-04-30

Published Online: 2011-04-14

Published in Print: 2011-11-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2011, Issue 660, Pages 99–130, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2011.070.

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