Lecture:2020/06/19,10:00-11:00,Yiqian Wang, Nanjing University

Date:2020-06-16Views:19

Speaker: Yiqian Wang from Nanjing University

Zoom ID: 87863513301, Code: 398342

Title: On quasi-periodic Schrodinger operators with cos-type potentials

Abstract: Quasiperiodic Schrodinger operators (QPSO) is the mathematical model for the conductivity on quasi-crystals which was found by a Nobel prize winner. Several great mathematicians have been captivated by this field.In last decades, various methods have been developed in the study of one-dimensional analytic QPSO, which led to a lot of deep result. However, these methods depend heavily on analytic conditions and are difficult to be extended to smooth situations. Recently we obtained a series of sharp results for Sinai's model (QPSO with a C^2 cos-type potential and a large coupling) . 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.