Abstract
We study one-dimensional, continuum Bernoulli-Anderson models with general single-site potentials and prove positivity of the Lyapunov exponent away from a discrete set of critical energies. The proof is based on Fürstenberg’s Theorem. The set of critical energies is described explicitly in terms of the transmission and reflection coefficients for scattering at the single-site potential. In examples we discuss the asymptotic behavior of generalized eigenfunctions at critical energies.
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Damanik, D., Sims, R., Stolz, G. (2002). Lyapunov Exponents in Continuum Bernoulli-Anderson Models. In: Albeverio, S., Elander, N., Everitt, W.N., Kurasov, P. (eds) Operator Methods in Ordinary and Partial Differential Equations. Operator Theory: Advances and Applications, vol 132. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8219-4_11
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DOI: https://doi.org/10.1007/978-3-0348-8219-4_11
Publisher Name: Birkhäuser, Basel
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