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It is known that a one-dimensional quantum particle is localized whensubjected to an arbitrarily weak random potential. It is conjectured thatlocalization also occurs for an arbitrarily weak potential generated from thenonlinear skew-shift dynamics: $v_n=2\cos\left(\binom{n}{2}\omega +ny+x\right)$with $\omega$ an irrational number. Recently, Han, Schlag, and the secondauthor derived a finite-size criterion in the case when $\omega$ is the goldenmean, which allows to derive the positivity of the infinite-volume Lyapunovexponent from three conditions imposed at a fixed, finite scale. Here wenumerically verify the two conditions among these that are amenable to computercalculations.

On the finite-size Lyapunov exponent for the Schroedinger operator with skew-shift potential