Anomalous quantum transportin presence of self-similar spectra

  title={Anomalous quantum transportin presence of self-similar spectra},
  author={J.-M. Barbaroux and Hermann Schulz-Baldes},
We consider nite-diierence Hamiltonians given by Jacobi matrices with self-similar spectra of the Cantor type and prove upper bounds on the diiusion exponents which show that the quantum motion in these models is anomalous diiusive. For Julia matrices, this bound is expressed only in terms of the generalized dimensions of the spectral measures. 

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