Transport Properties of Kicked and Quasiperiodic Hamiltonians |
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Authors: | S De Bièvre G Forni |
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Institution: | (1) UFR de Mathématiques et URA GAT, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France;;(2) Department of Mathematics, Princeton University, Princeton, New Jersey, 08544; |
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Abstract: | We study transport properties of Schrödinger operators depending on one or more parameters. Examples include the kicked rotor and operators with quasi-periodic potentials. We show that the mean growth exponent of the kinetic energy in the kicked rotor and of the mean square displacement in quasiperiodic potentials is generically equal to 2: this means that the motion remains ballistic, at least in a weak sense, even away from the resonances of the models. Stronger results are obtained for a class of tight-binding Hamiltonians with an electric field E(t) = E
0+ E
1cos t. For
with
we show that the mean square displacement satisfies
for suitable choices of , E
0, and E
1. We relate this behavior to the spectral properties of the Floquet operator of the problem. |
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Keywords: | Anomalous transport singular spectra kicked Hamiltonians |
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