[Seminar] [Seminar on Microlocal Analysis and Applications] Weyl laws for open quantum maps
Speaker： Zhenhao Li
Time： 10:00-11:00 am, 2022/05/06
zoom： 618 038 6257, Password: SCMS
Open quantum maps provide simple finite-dimensional models of open quantum chaos. They are families of $N \times N$ matrices that quantize a symplectic relation on a compact phase space, and their eigenvalues model resonances of certain open quantum systems in the semiclassical limit as $N \to \infty$. This makes them especially conducive to numerical experimentation and thus appealing in the study of scattering resonances. We consider a particular toy model that arises from quantizing the classical baker’s map. We find a Weyl upper bound in the semiclassical limit for the number of eigenvalues in a fixed annulus, and derive an explicit dependence on the radius of the annulus given Gevrey regularity. These results are accompanied by numerical experiments.