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- W2040252232 abstract "von Neumann has proved a quantum-mechanical ergodic theorem which deals with a closed macroscopic system and macroscopic observables. Certain unsatisfactory features of this theorem are probably due to the overly-strong idealization of a completely closed system.Since the claims of statistical mechanics go beyond macroscopic systems, there is a need for a more general theorem. The present paper deals with a system of any number of degrees of freedom and with any observable, during interaction with a temperature bath. In order to avoid an assumption of randomness, the bath must be described explicitly and precisely by a time-independent Hamiltonian. The model of the bath is obtained by taking the Gibbs ensemble seriously, i.e., as a set of $N$ identical systems interacting through a potential $ensuremath{lambda}V$.The following theorem is proved. The time average of the quantum-mechanical expectation value of any observable with respect to any initial state is equal to its statistical average, in the double limit $Nensuremath{rightarrow}ensuremath{infty}$, $ensuremath{lambda}ensuremath{rightarrow}0$, for the overwhelming majority of all interaction potentials $V$." @default.
- W2040252232 created "2016-06-24" @default.
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- W2040252232 date "1957-07-15" @default.
- W2040252232 modified "2023-09-25" @default.
- W2040252232 title "Ergodic Theorem for Interacting Systems" @default.
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- W2040252232 doi "https://doi.org/10.1103/physrev.107.333" @default.
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