主讲人： Akira Shudo

　　题  目："Exponential asymptotics and introduction to resurgent theory”

　　时  间：10月17日上午10点

　　地  点：理学院206

　　主  办：理学院

　　摘要：

　　Asymptotic expansions are used to provide approximate solutions of differential equations and to evaluate integrals with large (small) parameters. There are a variety of applications in which asymptotic expansions are efficient and powerful, but one deficiency of asymptotic expansions is that they are divergent  in general, and so there is no rigorous mathematical ground. This prevents us, for example, from exploring global relations connecting asymptotic expansions in different regions and one could get only local information.  It is also hard to control exponentially small quantities, which are sometimes physically significant (nonperturbative effects, tunneling, diffraction, ...).  Recent advances of resurgent theory (exponential asymptotics  beyond all orders, the exact WKB method) reveal that asymptotic expansions have rich information and exponentially small quantities can properly handled under a rigorous mathematical framework. One could extract even global information encoded in the remainder of asymptotic expansions. Here we introduce an idea of resurgent theory, focusing mainly on the saddle point analysis for integrals with a large (or small) parameter.  We also present an application of the resurgent analysis to quantum mechanics in chaotic systems.

　　个人简介: 

　　Akira Shudo is a Professor of Physics at Tokyo Metropolitan University in Japan.

　　He received his PhD from Waseda University. His research interests include statistical mechanics and mathematical physics in general, and more in particular quantum chaos, classical Hamiltonian dynamics, complex WKB analysis, and exotic quantum holonomy.  He is author of numerous publications in such journals as Physical Review Letters, Physical Review A, Physical Review E, and Journal of Physics A, which count more than 900 citations.