Localization for one dimensional, continuum, bernoulli-anderson models
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In this article, the authors used scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions, in particular the case of a Bernoulli dis- tribution.Abstract:
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli dis- tribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi-scale analysis. We show that non-reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.read more
Citations
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Journal ArticleDOI
On localization in the continuous Anderson-Bernoulli model in higher dimension
Jean Bourgain,Carlos E. Kenig +1 more
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Bootstrap Multiscale Analysis and Localization¶in Random Media
François Germinet,Abel Klein +1 more
TL;DR: In this paper, an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events is introduced. But the analysis is restricted to the case where the probability of the resolvent of the corresponding random operators is larger than 1 − e − e−ε.
An Invitation to Random Schr¨ odinger operators
TL;DR: The authors essayent de presenter les bases de la theorie des operateurs de Schrodinger aleatoires and present a demonstration complete des asymptotiques de Lifshitz and de la localisation d'Anderson.
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A characterization of the Anderson metal-insulator transport transition
François Germinet,Abel Klein +1 more
TL;DR: In this article, the Anderson metal-insulator transition for random Schrodinger operators is investigated and the strong insulator region is defined as the part of the spectrum where the random operator exhibits strong dynamical localization in the Hilbert-Schmidt norm.
Journal ArticleDOI
New Characterizations of the Region of Complete Localization for Random Schrödinger Operators
François Germinet,Abel Klein +1 more
TL;DR: In this article, the authors studied the region of complete localization in a class of random operators which includes random Schrodinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight binding model.
References
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