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Dynamics of the quasi-periodic Schrodinger cocycle at the lowest energy in the spectrum
2007 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 272, no 2, 397-442 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the quasi-periodic Schrodinger cocycle over T-d (d >= 1) and, in particular, its projectivization. In the regime of large coupling constants and Diophantine frequencies, we give an affirmative answer to a question posed by M. Herman [21, p.482] concerning the geometric structure of certain Strange Nonchaotic Attractors which appear in the projective dynamical system. We also show that for some phase, the lowest energy in the spectrum of the associated Schrodinger operator is an eigenvalue with an exponentially decaying eigenfunction. This generalizes [39] to the multi-frequency case (d > 1).

Place, publisher, year, edition, pages
2007. Vol. 272, no 2, 397-442 p.
Keyword [en]
anderson localization, integrated density, lyapunov exponents, rotation number, t-d, operators, equations, continuity, potentials, attractors
Identifiers
URN: urn:nbn:se:kth:diva-16787ISI: 000247964500003OAI: oai:DiVA.org:kth-16787DiVA: diva2:334830
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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