Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 351

Anomalous quantum transport in presence of self-similar spectra

Jean-Marie Barbaroux and Hermann Schulz-Baldes

We consider finite-difference Hamiltonians given by Jacobi matriceswith self-similar spectra of the Cantor type and prove upper bounds onthe diffusion exponents which show that the quantum motion in these models is anomalous diffusive. For Julia matrices, this bound is expressed only in terms of thegeneralized dimensions of the spectral measures.

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