School Colloquium——Quantum Chaos and Fractal Uncertainty Principle
报告人:Prof. Long Jin(Tsinghua University)
时间:2018-09-21 15:00-16:00
地点:Room 1114, Sciences Building No. 1
Abstract: In this talk, we discuss some recent development in the field of quantum chaos
via a new tool called fractal uncertainty principle. Roughly speaking, a fractal uncertainty
principle states that a function cannot be localized near fractal sets in both position and frequency.
It was first developed by Dyatlov-Zahl and Bourgain-Dyatlov to study spectral gaps and wave decay in
open quantum chaotic systems. In a joint work with Semyon Dyatlov, we also found its applications to
control and stabilization in closed quantum chaotic systems. In particular, we showed that Laplacian
eigenfunctions on compact hyperbolic surfaces cannot be completely localized in the high-frequency limit.