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. 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.Comment: 10 pages, 6 figures and 1 tabl
