Long-time behavior of macroscopic quantum systems: Commentary accompanying the English translation of John Von Neumann's 1929 article on the quantum ergodic theorem

Abstract
The 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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 12,088
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Similar books and articles
Analytics

Monthly downloads

Added to index

2010-03-03

Total downloads

28 ( #66,504 of 1,101,944 )

Recent downloads (6 months)

10 ( #24,823 of 1,101,944 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.