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December 2008 Positive Lyapunov exponents and localization bounds for strongly mixing potentials
Christian Sadel, Hermann Schulz-Baldes
Adv. Theor. Math. Phys. 12(6): 1377-1399 (December 2008).

Abstract

For a one-dimensional discrete Schrödinger operator with a weakly coupled potential given by a strongly mixing dynamical system with power law decay of correlations, we derive for all energies including the band edges and the band center a perturbative formula for the Lyapunov exponent. Under adequate hypothesis, this shows that the Lyapunov exponent is positive on the whole spectrum. This in turn implies that the Hausdorff dimension of the spectral measure is zero and that the associated quantum dynamics grows at most logarithmically in time.

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Christian Sadel. Hermann Schulz-Baldes. "Positive Lyapunov exponents and localization bounds for strongly mixing potentials." Adv. Theor. Math. Phys. 12 (6) 1377 - 1399, December 2008.

Information

Published: December 2008
First available in Project Euclid: 19 September 2008

zbMATH: 1151.81012
MathSciNet: MR2443267

Rights: Copyright © 2008 International Press of Boston

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Vol.12 • No. 6 • December 2008
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