On the approach to thermal equilibrium of macroscopic quantum systems

Sheldon Goldstein, Roderich Tumulka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In joint work with J. L. Lebowitz, C. Mastrodonato, and N. Zanghì [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+δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dimHeq/dimH is close to 1. We say that a system with state vector ψ ε H is in thermal equilibrium if ψ is "close" to Heq. We argue that for "typical" Hamiltonians, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This is closely related to von Neumann's quantum ergodic theorem of 1929.

Original languageEnglish (US)
Title of host publicationNon-Equilibrium Statistical Physics Today - Proceedings of the 11th Granada Seminar on Computational and Statistical Physics
Pages155-163
Number of pages9
DOIs
StatePublished - 2011
Event11th Granada Seminar on Computational and Statistical Physics - La Herradura, Spain
Duration: Sep 13 2010Sep 17 2010

Publication series

NameAIP Conference Proceedings
Volume1332
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other11th Granada Seminar on Computational and Statistical Physics
CountrySpain
CityLa Herradura
Period9/13/109/17/10

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • approach to thermal equilibrium
  • micro-canonical energy shell
  • quantum statistical mechanics
  • thermalization of closed macroscopic quantum systems
  • typical Hamiltonian
  • typical long-time behavior of quantum systems

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