Normal typicality and von Neumann’s quantum ergodic theorem

@article{Goldstein2010NormalTA,
  title={Normal typicality and von Neumann’s quantum ergodic theorem},
  author={Sheldon Goldstein and Joel L Lebowitz and Christian Mastrodonato and Roderich Tumulka and Nino Zangh{\'i}},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2010},
  volume={466},
  pages={3203 - 3224}
}
We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e. the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is ‘normal’: it evolves in such a way that |ψt⟩⟨ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The QET… 
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