A note on Lyapunov exponents of deterministic strongly mixing potentials

Abstract

In this Note, we consider 1D lattice Schrödinger operators with deterministic strongly mixing potentials as studied in [3] and [2] with very small coupling. We describe a scheme to establish positivity of the Lyapunov exponent from a statement at some fixed scale. The required input may then be derived from Furstenberg theory, if the underlying dynamics are sufficiently mixing, or verified directly by numerical means.