Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
We study the one-dimensional discrete Schrödinger operator with the skew-shift potential . This potential is long conjectured to behave like a random one, i.e., it is expected to produce Anderson localization for arbitrarily small coupling constants . In this paper, we introduce a novel perturbative approach for studying the zero-energy Lyapunov exponent at small . Our main results establish that, to second order in perturbation theory, a natural upper bound on is fully consistent with being positive and satisfying the usual Figotin-Pastur type asymptotics as . The analogous quantity behaves completely differently in the Almost-Mathieu model, whose zero-energy Lyapunov exponent vanishes for $\lambda
François Gallaire, Yves-Marie François Ducimetière
Frédéric Mila, Antoine Yves Dimitri Fache