Sadel, Christian; Schulz-Baldes, Hermann Positive Lyapunov exponents and localization bounds for strongly mixing potentials. (English) Zbl 1151.81012 Adv. Theor. Math. Phys. 12, No. 6, 1377-1399 (2008). Summary: 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. Cited in 3 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81Q15 Perturbation theories for operators and differential equations in quantum theory 34D08 Characteristic and Lyapunov exponents of ordinary differential equations × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid