# Normal Typicality and von Neumann&#x27;s Quantum Ergodic Theorem - Quantum Physics

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Abstract: We discuss the content and significance of John von Neumann-s quantum ergodictheorem QET of 1929, a strong result arising from the mere mathematicalstructure of quantum mechanics. The QET is a precise formulation of what wecall normal typicality, i.e., the statement that, for typical large systems,every initial wave function $\psi 0$ from an energy shell is -normal-: itevolves in such a way that $|\psi t> <\psi t|$ is, for most $t$,macroscopically equivalent to the micro-canonical density matrix. The QET hasbeen mostly forgotten after it was criticized as a dynamically vacuousstatement in several papers in the 1950s. However, we point out that thiscriticism does not apply to the actual QET, a correct statement of which doesnot appear in these papers, but to a different indeed weaker statement.Furthermore, we formulate a stronger statement of normal typicality, based onthe observation that the bound on the deviations from the average specified byvon Neumann is unnecessarily coarse and a much tighter and more relevantbound actually follows from his proof.

Autor: Sheldon Goldstein, Joel L. Lebowitz, Christian Mastrodonato, Roderich Tumulka, Nino Zanghi

Fuente: https://arxiv.org/