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We study the one-dimensional discrete Schrödinger operator with the skew-shift potential 2λcos(2π((2j)ω+jy+x)). This potential is long conjectured to be
We prove a conditional theorem on the positivity of the Lyapunov exponent for a Schrödinger cocycle over a skew shift base with a cosine potential and the golden ratio as frequency. For coupling below