Dynamical chaos – from KAM theorem to quantum Hall physics, SUSY and beyond
时间： 周五 16:30-17:30, 2019-12-27
The arising of chaos in deterministic dynamical systems is ubiquitous in nature. In this talk, I will show that dynamical chaos can give rise to topological quantum order and supersymmetry (SUSY), both of which are commonly conceived to be totally unrelated to chaos.
In the first part, I will introduce a canonical model of chaotic dynamics, the so-called kicked rotor (KR), and show how this model, though as simple as being a free rotating particle subjected to sequential external force pulses, displays rich dynamical phenomena. These range from weak chaoticity described by the Kolmogorov-Arnold-Moser theorem to dynamical localization, whose equivalence to Anderson localization in quantum disordered systems has attracted many attentions of distinguished mathematicians and mathematical physicists. In the second part, I will show how, by introducing a spin degree of freedom to KR, rich quantum dynamical behaviors of topological origin arise. They bear firm analogies to the quantum Hall effect and Haldane’s conjecture in many-electron systems and quantum antiferromagnetic chains, respectively. I will show how a SUSY structure is naturally embedded into KR, and serves as a seed for a wealth of topological quantum phenomena.
Dr. Tian did his Ph.D. studies under the supervision of late Prof. Anatoly I. Larkin (Landau Institute and Univ. of Minnesota) at Minnesota. He is a full professor of ITP/CAS and a senior visiting member of HKUST Jockey Club Institute for Advanced Study. His main research interests include non-integrable quantum dynamical systems, wave propagation and transport in random medium, the foundations of statistical mechanics, condensed matter field theory, and related mathematical physics. Dr. Tian received the Achievement in Asia Award from International Organization of Chinese Physicists and Astronomers (OCPA) at 2018 and the National Science Fund for Distinguished Young Scholars at 2019.