Absence of absolutely continuous spectrum for generic quasi-periodic Schrödinger operators on the real line

dc.citation.firstpage	783
dc.citation.journalTitle	Israel Journal of Mathematics
dc.citation.lastpage	796
dc.citation.volumeNumber	247
dc.contributor.author	Damanik, David
dc.contributor.author	Lenz, Daniel
dc.date.accessioned	2022-06-08T17:02:33Z
dc.date.available	2022-06-08T17:02:33Z
dc.date.issued	2022
dc.description.abstract	We show that a generic quasi-periodic Schrödinger operator in L2(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 Schrödinger operator with the resulting potential has empty absolutely continuous spectrum.
dc.identifier.citation	Damanik, David and Lenz, Daniel. "Absence of absolutely continuous spectrum for generic quasi-periodic Schrödinger operators on the real line." <i>Israel Journal of Mathematics,</i> 247, (2022) Springer Nature: 783-796. https://doi.org/10.1007/s11856-021-2280-4.
dc.identifier.doi	https://doi.org/10.1007/s11856-021-2280-4
dc.identifier.uri	https://hdl.handle.net/1911/112457
dc.language.iso	eng
dc.publisher	Springer Nature
dc.rights	This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer Nature.
dc.title	Absence of absolutely continuous spectrum for generic quasi-periodic Schrödinger operators on the real line
dc.type	Journal article
dc.type.dcmi	Text
dc.type.publication	pre-print

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