ergodicity การใช้

• Hence, strong mixing implies weak mixing, which implies ergodicity.
• Unique ergodicity of the flow was established by Hillel Furstenberg in 1972.
• Looking at the article ergodicity, I have a couple of questions.
• Another way ergodicity can be broken is by the existence of nonlinear soliton symmetries.
• That's probably an abuse on my part of the concept of ergodicity.
• The concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory.
• In 1939 Hopf established ergodicity of the geodesic flow on manifolds of constant negative curvature.
• He proved unique ergodicity of horocycle flows on compact hyperbolic Riemann surfaces in the early 1970s.
• Also conventional glasses ( e . g . window glasses ) violate ergodicity in a complicated manner.
• Mutation alone can provide ergodicity of the overall genetic algorithm process ( seen as a Markov chain ).
• Applications of ergodic theory to other parts of mathematics usually involve establishing ergodicity properties for systems of special kind.
• Likewise, you might consider trying to put issues of ergodicity and quantum failures above the more general formulation.
• :* Ergodicity is not a problem for the ultraviolet catastrophe, since all modes may be populated, no?
• This general phenomenon is called ergodicity .-- talk ) 06 : 16, 24 March 2008 ( UTC)
• The unique quantum ergodicity conjecture of Rudnick and Sarnak asks whether the stronger statement that individual eigenfunctions equidistribure is true.
• In short, thermalization could not occur because of a certain " soliton symmetry " in the system which broke ergodicity.
• The quantum ergodicity theorem of Shnirelman, Colin de Verdi鑢e and Zelditch states that on average, eigenfunctions equidistribute on S.
• The generalization is considered to be a good candidate for formulating a theory of non-non-ergodicity or metastable states.
• This constitutes a foundation for quantum statistical mechanics which is radically different from the one built upon the notions of dynamical ergodicity.
• Ergodicity is the assumption that a system, at a given temperature, explores the full phase space, just each state takes different probabilities.