Applications of ergodic theory to other parts of mathematics usually involve establishing ergodicity properties for systems of special kind.
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Likewise, you might consider trying to put issues of ergodicity and quantum failures above the more general formulation.
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:* Ergodicity is not a problem for the ultraviolet catastrophe, since all modes may be populated, no?
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This general phenomenon is called ergodicity .-- talk ) 06 : 16, 24 March 2008 ( UTC)
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The unique quantum ergodicity conjecture of Rudnick and Sarnak asks whether the stronger statement that individual eigenfunctions equidistribure is true.
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In short, thermalization could not occur because of a certain " soliton symmetry " in the system which broke ergodicity.
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The quantum ergodicity theorem of Shnirelman, Colin de Verdi�re and Zelditch states that on average, eigenfunctions equidistribute on S.
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The generalization is considered to be a good candidate for formulating a theory of non-non-ergodicity or metastable states.
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This constitutes a foundation for quantum statistical mechanics which is radically different from the one built upon the notions of dynamical ergodicity.
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Ergodicity is the assumption that a system, at a given temperature, explores the full phase space, just each state takes different probabilities.
