title: Ergodicity and mixing in quantum dynamics.
abstract: After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.
authors.affiliation: School of Physics, Peking University, Beijing 100871, China.
authors.forename: Dongliang
authors.initials: D
authors.lastname: Zhang
authors.affiliation: School of Physics, Peking University, Beijing 100871, China.|Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
authors.forename: H T
authors.initials: HT
authors.lastname: Quan
authors.affiliation: Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.|International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.|Wilczek Quantum Center, College of Science, Zhejiang University of Technology, Hangzhou 310014, China.
authors.forename: Biao
authors.initials: B
authors.lastname: Wu