Abstract
In the field of dynamical systems and nonlinear dynamics, little attentions have been paid to the impacts of the quantum spin degree of freedoms. In this seminar, I shall review recent results showing that it can totally change the behaviors of some canonical models in chaotic dynamics, and gives rise to rich quantum dynamical phenomena of topological origin. These phenomena indicate that spinful dynamical systems carry a wealth of new mathematical structures, ranging from quantum topology and spectral properties to supersymmetry.
In the first part, I will introduce two models, the kicked rotor and the Maryland model, widely studied by mathematicians and physicists. I will review the foundational result in the studies of these two models, namely, the so-called dynamical localization, which is an analog of localization in quantum disordered or incommensurate systems. In the second and the third parts, I will show that this foundation result is completely destroyed in the presence of SU(2) spin. In the second part, I will review the topological supersymmetry field theory developed for the spinful kicked rotor, and use that theory to show that instead of dynamical localization a phenomenon analogous to the celebrated integer quantum Hall effect occurs. In the third part, I will review some rigorous mathematical results for the spin-Maryland model, which belongs to the class of skew product systems on T2 × SU(2), obtained by the operator theory. These results uncover a dynamical localization-delocalization transition triggered by the self-duality, which falls into the same class of topological transition in quantum Hall physics.
In the first part, I will introduce two models, the kicked rotor and the Maryland model, widely studied by mathematicians and physicists. I will review the foundational result in the studies of these two models, namely, the so-called dynamical localization, which is an analog of localization in quantum disordered or incommensurate systems. In the second and the third parts, I will show that this foundation result is completely destroyed in the presence of SU(2) spin. In the second part, I will review the topological supersymmetry field theory developed for the spinful kicked rotor, and use that theory to show that instead of dynamical localization a phenomenon analogous to the celebrated integer quantum Hall effect occurs. In the third part, I will review some rigorous mathematical results for the spin-Maryland model, which belongs to the class of skew product systems on T2 × SU(2), obtained by the operator theory. These results uncover a dynamical localization-delocalization transition triggered by the self-duality, which falls into the same class of topological transition in quantum Hall physics.
Biography
Dr. Chushun Tian is a full professor in ITP/CAS. His main research interests are disordered systems, chaotic dynamics, the foundations of statistical mechanics, and related mathematical physics.
(Joint Seminar of the Department of Physics & HK Institute of Quantum Science & Technology)
Anyone interested is welcome to attend.