Method of variations of potential of quasi-periodic Schrodinger equation

Physics – Mathematical Physics

Scientific paper

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Scientific paper

We study the one-dimensional discrete quasi-periodic Schrodinger equation. We
introduce the notion of variations of potential and use it to define "typical"
potential. We show that for typical C^3 potential, if the coupling constant is
large, then for most frequencies, the Lyapunov exponent is positive for all
energies.

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