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Title:
Multiscale Analysis in Momentum Space for Multi-Dimensional Quasi-Periodic Schrodinger Operators
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Abstract:
We consider Schrödinger operators H = −∆+V (x) in Rd, d ≥ 2, withquasi-periodic potentials V (x). We prove that the absolutely continuous spectrumof a generic H contains a semi-axis [λ∗, ∞). We also construct a family of eigenfunctions of the absolutely continuous spectrum; these eigenfunctions are smallperturbations of the exponentials. The proof is based on the multi-scale analysisin the momentum space.
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