On the approach to thermal equilibrium of macroscopic quantum systems

Journal Article · Thu Mar 24 04:00:00 EDT 2011 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3577619· OSTI ID:21511480

Goldstein, Sheldon ^[1]; Tumulka, Roderich ^[2]

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1. Departments of Mathematics and Physics, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States)
2. Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States)

In joint work with J. L. Lebowitz, C. Mastrodonato, and N. Zanghi[2, 3, 4], we considered an isolated, macroscopic quantum system. Let H be a micro-canonical 'energy shell', i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E+{delta}E. The thermal equilibrium macro-state at energy E corresponds to a subspace H{sub eq} of H such that dimHeq/dimH is close to 1. We say that a system with state vector {psi}{epsilon}H is in thermal equilibrium if {psi} is 'close' to H{sub eq}. We argue that for 'typical' Hamiltonians, all initial state vectors {psi}{sub 0} evolve in such a way that {psi}{sub t} is in thermal equilibrium for most times t. This is closely related to von Neumann's quantum ergodic theorem of 1929.

• OSTI ID: 21511480
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1332; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

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