Localization for an Anderson-Bernoulli model with generic interaction potential

Details Localization for an Anderson-Bernoulli model with generic interaction potential Localization for an Anderson-Bernoulli model with generic interaction potential

2010-06-11

arxiv.org/abs/1006.2286v1

Mathematics

Spectral Theory

11 pages

Scientific paper

We present a result of localization for a matrix-valued Anderson-Bernoulli operator, acting on $L^2(\R)\otimes \R^N$, for an arbitrary $N\geq 1$, whose interaction potential is generic in the real symmetric matrices. For such a generic real symmetric matrix, we construct an explicit interval of energies on which we prove localization, in both spectral and dynamical senses, away from a finite set of critical energies. This construction is based upon the formalism of the F\"urstenberg group to which we apply a general criterion of density in semisimple Lie groups. The algebraic nature of the objects we are considering allows us to prove a generic result on the interaction potential and the finiteness of the set of critical energies.

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