Lyapunov exponents in continuum Bernoulli-Anderson models

Details Lyapunov exponents in continuum Bernoulli-Anderson models Lyapunov exponents in continuum Bernoulli-Anderson models

2001-01-11

arxiv.org/abs/math-ph/0101011v1

Physics

Mathematical Physics

11 pages

Scientific paper

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 F\"urstenberg'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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