Explicit examples of arbitrarily large analytic ergodic potentials with zero Lyapunov exponent

Abstract.

We give explicit examples of arbitrarily large analytic ergodic potentials for which the Schrödinger equation has zero Lyapunov exponent for certain energies. For one of these energies there is an explicit solution. In the quasi-periodic case we prove that one can have positive Lyapunov exponent on certain regions of the spectrum and zero on other regions. We also show the existence of 1-dependent random potentials with zero Lyapunov exponent.