98-733 A. Fedotov and F. Klopp

Anderson transitions for quasi-periodic Schr dinger operators in dimension 1 (460K, Gzipped Postscript) Nov 27, 98

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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. We show that the spectrum is located in exponentially small intervals whose centers are described by Bohr-Sommerfeld like conditions. We give a sufficient condition for the existence of absolutely continuous spectrum as well as for the existence of singular spectrum. We use this condition to study the coexistence of both spectral types. This enables us to define asymptotic mobility edges and study their locus.

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