Lingrui Ge (UCI)
Quantitative almost reducibility and its spectral applications
Abstract:
We report our recent progresses on quantitative almost
reducibility (QAR) for quasiperiodic $SL(2,\R)$-cocycles. As
applications, we will explain how to use QAR to obtain arithmetic
version of Anderson localization, exponential dynamical localization,
ballistic transport, asymptotical estimates of spectral gaps and
universal hierarchical structure of generalized eigenfunctions for
quasiperiodic Schr\"odinger operators (especially for the almost Mathieu
operator).
This is based on joint works with Ilya Kachkovskiy, Jiangong You, Xin
Zhao and Qi Zhou.