Normal Typicality and von Neumann's Quantum Ergodic Theorem

Normal Typicality and von Neumann's Quantum Ergodic Theorem

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2010-04
Hauptverfasser: Goldstein, Sheldon, Lebowitz, Joel L, Mastrodonato, Christian, Tumulka, Roderich, Zanghi, Nino
Format: Artikel
Sprache:eng
Schlagworte:
Ergodic processes
Mathematical analysis
Matrix methods
Physics - Quantum Physics
Physics - Statistical Mechanics
Quantum mechanics
Theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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 \(\psi_0\) from an energy shell is "normal": it evolves in such a way that \(|\psi_t>
ISSN:2331-8422
DOI:10.48550/arxiv.0907.0108