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Pré-Publication, Document De Travail Année : 2017

Asymptotics of spectral gaps of quasi-periodic Schr\"odinger operators

Martin Leguil
Jiangong You
  • Fonction : Auteur
Zhiyan Zhao
  • Fonction : Auteur
  • PersonId : 1067225
Qi Zhou

Résumé

For non-critical almost Mathieu operators with Diophantine frequency, we establish exponential asymptotics on the size of spectral gaps, and show that the spectrum is homogeneous. We also prove the homogeneity of the spectrum for Sch\"odinger operators with (measure-theoretically) typical quasi-periodic analytic potentials and fixed strong Diophantine frequency. As applications, we show the discrete version of Deift's conjecture \cite{Deift, Deift17} for subcritical analytic quasi-periodic initial data and solve a series of open problems of Damanik-Goldstein et al \cite{BDGL, DGL1, dgsv, Go} and Kotani \cite{Kot97}.

Dates et versions

hal-03380272 , version 1 (15-10-2021)

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Martin Leguil, Jiangong You, Zhiyan Zhao, Qi Zhou. Asymptotics of spectral gaps of quasi-periodic Schr\"odinger operators. 2017. ⟨hal-03380272⟩
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