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Register a new userAbsence of Absolutely Continuous Spectrum for Generic Quasi-Periodic Schrodinger Operators on the Real Line
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Authors
David Damanik
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We show that a generic quasi-periodic Schrodinger operator in $L^2(mathbb{R})$ has purely singular spectrum. That is, for any minimal translation flow on a finite-dimensional torus, there is a residual set of continuous sampling functions such that for each of these sampling functions, the Schrodinger operator with the resulting potential has empty absolutely continuous spectrum.
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We give sufficient conditions for the presence of the absolutely continuous spectrum of a Schrodinger operator on a regular rooted tree without loops (also called regular Bethe lattice or Cayley tree).
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