01-224 Alexander Fedotov and Fr d ric Klopp

On the absolutely continuous spectrum of one dimensional quasi-periodic Schr dinger operators in the adiabatic limit (469K, Postscript) Jun 22, 01

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Abstract. In this paper we study the spectral properties of families of quasi-periodic Schr dinger operators on the real line in the adiabatic limit in the case when the adiabatic iso-energetic curves are extended along the position direction. We prove that, in energy intervals where this is the case, most of the spectrum is purely absolutely continuous in the adiabatic limit, and that the associated generalized eigenfunctions are Bloch-Floquet solutions.

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