Speaker: 许珈豪, 北京大学 访问助理教授
Inviter: 夏旭
Title: Geometry Conditions On Quasi-Periodic Schrödinger Operators (QPSO)
Time & Venue: 2025.08.02 10:10-11:10 思源楼 615
Abstract: In this talk we will introduce our results on cosine-like QPSOs and discuss the roles played by geometry condition in QSPOs. Under a specific geometry condition (cosine-like) with a weak regularity condition ($C^2$), we showed that for a large coupling and Diophantine frequency, the Lyapunov exponent (LE) is $1/2$-Hölder and absolutely continuous with respect to the energy, and all the spectral gaps are open; while for the analytic case, the regularity of LE can be less than $\epsilon$-Hölder continuous for any $\epsilon > 0$.
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