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Anomalous quantum transport in presence of self-similar spectra. (English) Zbl 1076.82531

Summary: We consider finite-difference Hamiltonians given by Jacobi matrices with self-similar spectra of the Cantor type and prove upper bounds on the 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 the generalized dimensions of the spectral measures.

MSC:

82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
47N50 Applications of operator theory in the physical sciences
81Q99 General mathematical topics and methods in quantum theory
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