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تسجيل مستخدم جديدOn the finite-size Lyapunov exponent for the Schroedinger operator with skew-shift potential
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It is known that a one-dimensional quantum particle is localized when subjected to an arbitrarily weak random potential. It is conjectured that localization also occurs for an arbitrarily weak potential generated from the nonlinear skew-shift dynamics: $v_n=2cosleft(binom{n}{2}omega +ny+xright)$ with $omega$ an irrational number. Recently, Han, Schlag, and the second author derived a finite-size criterion in the case when $omega$ is the golden mean, which allows to derive the positivity of the infinite-volume Lyapunov exponent from three conditions imposed at a fixed, finite scale. Here we numerically verify the two conditions among these that are amenable to computer calculations.
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