Long-time behavior of macroscopic quantum systems
By Sheldon Goldstein, J. Lebowitz, Roderich Tumulka, Nino Zanghí. 2010
165 citations recorded by the source corpus.
AbstractThe renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the “quantum H-theorem”, is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the “quantum ergodic theorem”, is a beautiful and very non-trivial result. It expresses a fact we call “normal typicality” and can be summarized as follows: for a “typical” finite family of commuting macroscopic observables, every initial wave function ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψt is close to their micro-canonical distribution.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8e5b368c62a88d6e208040e0a89e805c00074807
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In Atomic and Molecular Physics, and Optics
- Alessandro Silva
- M. Vengalattore
- K. Sengupta
- A. Polkovnikov
- Pasquale Calabrese
- V. Gritsev
- Brian Swingle
- Shenglong Xu
In Statistical and Nonlinear Physics
Citations in the corpus
- Local random quantum circuits are approximate polynomial-designs: numerical results (2012, unknown): “[33]).”
- Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, background): “In particular, for every | Ψ0〉 and almost every set {Mβ} the diagonal and microcanonical ensembles are equivalent (Goldstein et al., 2010; von Neumann, 1929).”