Normal typicality and Von Neumann's quantum ergodic theorem
| Abstract | 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 has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s. However, we point out that this criticism does not apply to the actual QET, a correct statement of which does not appear in these papers, but to a different (indeed weaker) statement. Furthermore, we formulate a stronger statement of normal typicality, based on the observation that the bound on the deviations from the average specified by von Neumann is unnecessarily coarse and a much tighter (and more relevant) bound actually follows from his proof. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,875 |
| External links |
  Try with proxy. Try with proxy. Try with proxy. |
| Through your library | Only published papers are available at libraries |
Similar books and articlesJ. B. Kennedy (1995). On the Empirical Foundations of the Quantum No-Signalling Proofs. Philosophy of Science 62 (4):543-560.
Jan von Plato (1982). The Significance of the Ergodic Decomposition of Stationary Measures for the Interpretation of Probability. Synthese 53 (3):419 - 432.
Lon Becker (2004). That Von Neumann Did Not Believe in a Physical Collapse. British Journal for the Philosophy of Science 55 (1):121-135.
Leah Henderson (2003). The Von Neumann Entropy: A Reply to Shenker. British Journal for the Philosophy of Science 54 (2):291-296.
Analytics
Monthly downloads |
Added to index2009-07-04Total downloads15 ( #79,694 of 556,837 )Recent downloads (6 months)1 ( #64,847 of 556,837 )How can I increase my downloads? |
My notes
Discussion
