Article
Licensed
Unlicensed
Requires Authentication
A continuum version of the Kunz–Souillard approach to localization in one dimension
-
David Damanik
and
Günter Stolz
Published/Copyright:
April 14, 2011
Abstract
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.
Received: 2010-02-08
Revised: 2010-04-30
Published Online: 2011-04-14
Published in Print: 2011-November
© Walter de Gruyter Berlin · New York 2011
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Serre weights for mod p Hilbert modular forms: the totally ramified case
- On the regulator of Fermat motives and generalized hypergeometric functions
- Badly approximable systems of affine forms, fractals, and Schmidt games
- A continuum version of the Kunz–Souillard approach to localization in one dimension
- The Bohr radius of the unit ball of
- On positive solutions of some system of reaction-diffusion equations with nonlocal initial conditions
- The rigidity of embedded constant mean curvature surfaces
- Isothermic submanifolds of symmetric R-spaces
Articles in the same Issue
- Serre weights for mod p Hilbert modular forms: the totally ramified case
- On the regulator of Fermat motives and generalized hypergeometric functions
- Badly approximable systems of affine forms, fractals, and Schmidt games
- A continuum version of the Kunz–Souillard approach to localization in one dimension
- The Bohr radius of the unit ball of
- On positive solutions of some system of reaction-diffusion equations with nonlocal initial conditions
- The rigidity of embedded constant mean curvature surfaces
- Isothermic submanifolds of symmetric R-spaces
