- 05-197 Domingos H. U. Marchetti, Walter F. Wreszinski, Leonardo F. Guidi, Renato M. Angelo
- Off-Diagonal Jacobi Matrices as a Model for a Spectral Transition of Anderson Type
May 31, 05
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Abstract. We introduce a class of Jacobi matrices which model a deterministic (sparse) disorder in the sense that the perturbation of the Laplacean consists of a(direct) sum of fixed off-diagonal two by two matrices placed at sites whose distances from one another grow exponentially. We prove that the spectrum is the set [-2,2]. For "small coupling" there is (dense) pure point spectrum and for "large coupling" the support of the singular continuous spectral measure contains a set of positive Lebesgue measure, if the Pr fer angles are uniformly distributed. There is compelling numerical evidence for the latter property, which is briefly discussed.