Ergodicity and Mixing in Quantum Dynamics

Dongliang Zhang, H. T. Quan, Biao Wu

Published 2016-01-04Version 1

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 usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced; their relations to quantum ergodicity and mixing are demonstrated with right triangular billiards. With this billiard system, we find that a system is ergodic in its quantum dynamics may not be ergodic in its classical dynamics. 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.