Absence of Eigenvalues of Analytic Quasi-Periodic Schrödinger Operators on Rd.

In this paper we study the Schrödinger operator H = - Δ + λ V (x) with a real analytic quasi-periodic potential V (x) defined on R d for arbitrary d ≥ 1 . We prove that H has no eigenvalues in the energy interval - | log λ | C , | log λ | C for every C > 0 if λ > 0 is sufficiently small. The proof is based on the Aubry duality and the multi-scale analysis in the momentum space. [ABSTRACT FROM AUTHOR]