Sadel CH, Schulz-Baldes H (2008)
Publication Type: Journal article
Publication year: 2008
Publisher: International Press
Book Volume: 12
Pages Range: 1377-1400
URI: http://de.arxiv.org/abs/math-ph/0702052
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. © 2008 International Press.
APA:
Sadel, C.H., & Schulz-Baldes, H. (2008). Positive Lyapunov exponents and localization bounds for strongly mixing potentials. Advances in Theoretical and Mathematical Physics, 12, 1377-1400.
MLA:
Sadel, Christian Hermann, and Hermann Schulz-Baldes. "Positive Lyapunov exponents and localization bounds for strongly mixing potentials." Advances in Theoretical and Mathematical Physics 12 (2008): 1377-1400.
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