Method of Variations of Potential of Quasi-periodic Schrödinger Equation
نویسنده
چکیده
We study the one-dimensional discrete quasi-periodic Schrödinger equation −φ(n+ 1) − φ(n− 1) + λV (x+ nω)φ(n) = Eφ(n), n ∈ Z We introduce the notion of variations of potential and use it to define “typical” potential. We show that for “typical” C potential V , if the coupling constant λ is large, then for most frequencies ω, the Lyapunov exponent is positive for all energies E.
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