報告題目：Applying solid state physics to classical waves: Bound states in the continuum and non-Hermitian physics
報 告 人：Dr. Yixin Xiao (Hong Kong University of science and technology）
This report comprises two parts: one is about bound states in the continuum, and the other is about non-Hermitian physics. Bound states in the continuum are eigenstates (waves) that remain localized even though they coexist with a continuous spectrum of extended eigenstates (radiating waves in the context of wave systems). In this talk I will introduce the existence of bound states in the continuum in two kinds of systems: one utilizes the concept of topological subspace, and the other uses Anderson localization. Bound states come from topological interface states and Anderson localized states, respectively, in these two systems. In the second part, I will introduce some interesting phenomena in non-Hermitian systems. The most prominent phenomenon in non-Hermitian systems is the occurrence of exceptional points, where several eigenvalues as well as their eigenvectors coalesce. I will first introduce the phenomenon of anisotropic exceptional points of arbitrary order and exceptional ellipses in a 1D system with asymmetric hoppings. Universal power laws for the asymptotic behaviors of both eigenvalues and phase rigidities will be shown. Next I will introduce the phenomenon that exceptional points form a star-like shape in the Lieb lattice with gain/loss added. The evolution behavior of the exceptional points will be shown. A topological invariant called the discriminant number is used to characterize the robustness and creation/annihilation of some discrete exceptional points.
Yi-Xin XIAO is currently a postdoc researcher at Hong Kong University of Science and Technology. He obtained his Ph. D. from the Hong Kong University of Science and Technology (Advisor: Prof. C. T. Chan) and bachelor’s degree from Wuhan University. Dr. Xiao is now working on non-Hermitian systems and the topological properties therein.