Ergodicity and mixing in quantum dynamics
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 …
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 …
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.
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