* Title: Non-Hermitian physics and non-Hermitian singularity

 

* Speaker: Jung-Wan Ryu (IBS, Center for Theoretical Physics of Complex Systems)

 

 

Abstract: We will introduce non-Hermitian phenomena and non-Hermitian degeneracy, i.e., exceptional point (EP), which are ubiquitous in various physical systems. We will also discuss classifications of multiple arbitrary-order EPs by invoking the permutation group and its conjugacy classes [1]. We classify topological structures of Riemann surfaces generated by multiple states around multiple arbitrary-order EPs, using the permutation properties of stroboscopic encircling EPs. All possible permutations of products of holonomy matrices describing encircling a 2nd-order EP are revealed and classified into finite numbers of classes according to the topological structures of Riemann surfaces. Finally, the results are realized in non-Hermitian effective Hamiltonian based on Jordan normal forms and fully desymmetrized optical microcavities.

 

 [1] Jung-Wan Ryu, Jae-Ho Han, and Chang-Hwan Yi, Classification of multiple arbitrary-order non-Hermitian singularities, Phys. Rev. A 106, 012218 (2022).