Localization for an Anderson-Bernoulli model with generic interaction potential
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In this paper, the authors present a result of localization for a matrix-valued Anderson-Bernoulli operator acting on the space of ρ-valued square-integrable functions, for an arbitrary $N$ larger than 1.Abstract:
We present a result of localization for a matrix-valued Anderson-Bernoulli operator acting on the space of $\boldsymbol{C}^N$-valued square-integrable functions, for an arbitrary $N$ larger than 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 Furstenberg 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.read more
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Absence of absolutely continuous spectrum for random scattering zippers
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References
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TL;DR: In this article, the multiplicative ergodic theorem on Lyapunov indices of a difference matrix Schrodinger equation is generalized to the multiplicity of indices. But this result is not applicable to the case of a semigroup.
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