Absence of eigenvalues for quasiperiodic Schrödinger type operators

Abstract

We obtain the matrix-valued Schrödinger-type operators [H_α,θ] with Lipschitz potentials having no eigenvalues on the set {E: L(E)<δ_C,d(α,θ)}, where δ is an explicit function depending on the sampling function C(θ), dimension d, phase θ, and frequency α, and L(E) is the Lyapunov exponent.

Keywords

Quasiperiodic Schrödinger type operators / absence of eigenvalues / singular continuous spectrum

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