TY - JOUR
T1 - Localization for one-dimensional, continuum, Bernoulli-Anderson models
AU - Damanik, David
AU - Sims, Robert
AU - Stolz, Günter
PY - 2002/7/15
Y1 - 2002/7/15
N2 - 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 distribution 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 nonreflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.
AB - 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 distribution 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 nonreflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.
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U2 - 10.1215/S0012-7094-02-11414-8
DO - 10.1215/S0012-7094-02-11414-8
M3 - Article
AN - SCOPUS:0037099097
SN - 0012-7094
VL - 114
SP - 59
EP - 100
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -