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We use scattering theoretic methods to prove strong dynamical and exponential local- ization for one-dimensional, continuum, Anderson-type models with singular distri- butions; 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 sin- gle sites lead to a discrete set of exceptional energies away from which localization occurs.

Localization for one-dimensional, continuum, Bernoulli-Anderson models