Absolutely continuous spectrum for 1D quasiperiodic operators

By Jean Bourgain, S. Jitomirskaya. 2002

126 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b414f19780b7bab65679dbdcf9db1c81575e4c77

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Schrödinger operators with dynamically defined potentials (2014, background): “Such an improvement was obtained by Jitomirskaya and Last in [136] for λ > 14.5 and by Jitomirskaya and Krasovsky in [134] for λ > 1 (really as a consequence of L(E) > 0, which by the Herman estimate holds when λ > 1).”
Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications (2012, background): “Avila and Jitomirskaya [7] further developed a quantitative Aubry duality to prove that almost localization implies almost reducibility for the dual model.”
Generic Singular Spectrum For Ergodic Schrödinger Operators (2005, background): “We thank Svetlana Jitomirskaya and Barry Simon for stimulating discussions.”
Almost reducibility and absolute continuity I (2010, background): “requency cocycle close to constant is almost reducible. Proof. Any one-frequency cocycle which is close to constant is either uniformly hyperbolic or subcritical (this is essentially due to [BJ1] and [BJ2], and it is explicitly obtained in [A1] by a diﬀerent argument). Uniformly hyperbolic cocycles ”
Almost localization and almost reducibility (2008, methodology): “v,λbe as in Theorem 1.4. Then the singular spectrum is the same for all phases θ∈ R(and empty). We note that in the non-perturbative regime, the a.e. absolutely continuous spectrum was established in [BJ1]. What we address here is the stability of singular spectrum. 1.3. Further non-perturbative ana”