A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with two-body forces between the constituents or it may be a quantum billiard without any two-body forces. Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points in the complex plane. Under certain conditions, these branch points appear as double poles of the $S$ matrix. They influence the dynamics of open as well as of closed quantum systems. The dynamics of the two-level system is studied in detail analytically as well as numerically.
Probing Stringy Horizons with Pole-Skipping in Non-Maximal Chaotic Systems
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学 Kavli理论科学研究院）；MIT Center for Theoretical Physics—a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）
Pole Placement Approach to Coherent Passive Reservoir Engineering for Storing Quantum Information
The Australian National University（澳大利亚国立大学）；INRIA Paris（法国国家信息与自动化研究所巴黎分部）；Zhejiang University（浙江大学）；CNRS, Laboratoire des signaux et systèmes (L2S), CentraleSupélec（法国国家科学研究中心信号与系统实验室（L2S），中央理工-高等电力学院）；University of New South Wales at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院）
Broadband bright biphotons from periodically poled triple-resonance metasurface
Songshan Lake Materials Laboratory（松山湖材料实验室）；ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Department of Electronic Materials Engineering, Research School of Physics, Australian National University（澳大利亚国立大学变革性超光学系统卓越中心（TMOS）电子材料工程系物理研究学院）；School of Physics, Nanjing University（南京大学物理学院）；Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学应用物理研究所阿贝光子学中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）
