Almost localization and almost reducibility

作者：Avila A^*; Jitomirskaya S

来源：Journal of the European Mathematical Society, 2010, 12(1): 93-131.

DOI：10.4171/jems/191

• Quasiperiodic Schrodinger operators
• Anderson localization
• reducibility
• absolutely continuous spectrum

We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schrodinger cocycles associated to a non-perturbatively small analytic potential and Diophantine frequency. In particular, we establish the full version of Eliasson's reducibility theory in this regime (our approach actually leads to improvements even in the perturbative regime: we are able to show, for all energies, "almost reducibility" in some band of analyticity). We also prove 1/2-Holder continuity of the integrated density of states. For the almost Mathieu operator, our results hold through the entire regime of subcritical coupling and imply also the dry version of the Ten Martini Problem for the relevant parameters.

• 出版日期2010