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Report | Quantum Ergodicity and Mixing

Quantum Ergodicity and Mixing

Speaker: Prof. Biao Wu (Beijing University) 

Time: Sep 05, 2018 (Wed), 4:00-5:00pm

Location: Room 437, Xingjian Building 

Host: Center for Quantum Transport and Thermal Energy Science, School of Physics and Technology

Abstract: Although quantum dynamics is linear, it can be very complex. We show that the complexity of quantum dynamics can be classified in the similar spirit that the complexity of classical dynamics is classified. We first give an overview of classical ergodic hierarchy, with emphasis on ergodicity and mixing of classical dynamics.  We then introduce new definitions for quantum ergodicity and mixing, which are inspired by von Neumann’s work in 1929 and involve only the energy eigenvalues of a given quantum system. We show that these new definitions are consistent with our usual intuitive understanding of ergodicity and mixing. In particular, we show with quantum kicked rotor that our definitions are consistent with classical ergodicity and mixing in the semiclassical limit. 

References: 
[1] D. Zhang, H. T. Quan, and B. Wu, Physical Review E 94, 022150 (2016)
[2] J. Jiang, Y. Chen, and B. Wu, arXiv:1712.04533 (2017).