Generalization of von Neumann's Approach to Thermalization

Abstract

Thermalization of isolated many-body systems is demonstrated by generalizing an approach originally due to von Neumann: For arbitrary initial states with a macroscopically well-defined energy, quantum mechanical expectation values become indistinguishable from the corresponding microcanonical expectation values for the overwhelming majority of all sufficiently late times. As in von Neumann's work, the eigenvectors of the Hamiltonian and of the considered observable are required to not exhibit any specially tailored (untypical) orientation relative to each other. But all of von Neumann's further assumptions about the admitted observables are abandoned.

References in corpus (5)

• Thermalization and its mechanism for generic isolated quantum systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Typicality for Generalized Microcanonical Ensembles
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem

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• Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize
• Transportless equilibration in isolated many-body quantum systems
• Saturation of entropy production in quantum many-body systems
• Theoretical study on thermalization in isolated quantum systems