On quasiperiodic Schrödinger operators with a C^2 cos-type potential and a large coupling
报告人：Yiqian Wang (Nanjing University)
地点：Room 1513, Sciences Building No. 1
Abstract: In last decades, various methods have been developed in the study of one-dimensional (discrete) quasiperiodic Schrödinger operators (QPSO) under an analytic condition. Based on them, a lot of deep results on spectrum of analytic QPSO. However, these methods depend heavily on analytic conditions and are diﬃcult to be extended to smooth situations. Recently a series of sharp results for Sinai's model (QPSO with a C2 cos-type potential and a large coupling) were obtained, which improved the results obtained by Y. Wang and Z. Zhang. More precisely, they include a sharp estimate on the regularity of Lyapunov exponents (which is even new for Almost Mathieu operator with a cosine potential), the dry version of Cantor spectrum, homogenous spectrum gap and absolute continuity of IDS.