Positive lyapunov exponent and minimality for the continuous 1-d quasi-periodic Schrodinger equation with two basic frequencies
2007 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 8, no 4, 687-730 p.Article in journal (Refereed) Published
We consider the time-independent quasi-periodic Schrodinger equation [GRAPHICS] with a potential function V : T-2 -> R of class C-2 with a unique non-degenerate global minimum, large coupling constants K-2 and energies E in the bottom of the spectrum of the associated Schrodinger operator. We obtain estimates on the Lyapunov exponents and the Lebesgue measure of the spectrum, as well as localization results. Moreover, we show that the projective flow on T-2 x P-1 induced by the Schrodinger equation often is minimal.
Place, publisher, year, edition, pages
2007. Vol. 8, no 4, 687-730 p.
IdentifiersURN: urn:nbn:se:kth:diva-16806ISI: 000248120800002OAI: oai:DiVA.org:kth-16806DiVA: diva2:334849
QC 201005252010-08-052010-08-05Bibliographically approved