Relaxation into equilibrium under pure Schrödinger dynamics

OriginalPaper

Abstract.

We consider bipartite quantum systems that are described completely by a state vector \(\vert{\Psi(t)}\rangle\) and the fully deterministic Schrödinger equation. Under weak constraints and without any artificially introduced decoherence or irreversibility, the smaller of the two subsystems shows thermodynamic behaviour like relaxation into an equilibrium, maximization of entropy and the emergence of the Boltzmann energy distribution. This generic behaviour results from entanglement.

Keywords

Entropy Energy Distribution State Vector Quantum System Generic Behaviour 

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References

  1. 1.
    L. Landau, M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1968)Google Scholar
  2. 2.
    J. von Neumann, Z. Phys. 57, 30 (1929)MATHGoogle Scholar
  3. 3.
    G. Lindblad, Non-equilibrium Entropy and Irrevers. (D. Reidel Publish. Comp., Dordrecht, 1983)Google Scholar
  4. 4.
    P. Davies, The physics of time asymmetry (Univ. of Calif. Pr., Berkeley, 1974)Google Scholar
  5. 5.
    H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, Berlin, 1993)Google Scholar
  6. 6.
    U. Weiss, Quantum dissipative systems (World Scientific, Singapore, 1999)Google Scholar
  7. 7.
    J. Gemmer, A. Otte, G. Mahler, Phys. Rev. Lett. 86, 1927 (2001)CrossRefGoogle Scholar
  8. 8.
    J. Gemmer, G. Mahler, Eur. Phys. J. B 31, 249 (2003)Google Scholar
  9. 9.
    H. Tasaki, Phys. Rev. Lett. 80, 1373 (1998)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    K. Saito, S. Takesue, S. Miyashita, J. Phys. Soc. Jpn 65, 1243 (1996)Google Scholar
  11. 11.
    R.V. Jensen, R. Shankar, Phys. Rev. Lett. 54, 1879 (1985)CrossRefGoogle Scholar
  12. 12.
    F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991), p. 40Google Scholar
  13. 13.
    W. Brenig, Statistische Theorie der Wärme (Springer, Berlin, 1996)Google Scholar
  14. 14.
    G.M. Wang, E.M. Sevick, E. Mittag, D.J. Searles, D.J. Evans, Phys. Rev. Lett. 89, 050601 (2002)CrossRefGoogle Scholar
  15. 15.
    J. Gemmer, Ph.D. thesis (unpublished, Stuttgart, 2003)Google Scholar
  16. 16.
    T. Opatrný, M.O. Scully, Fortschr. Phys. 50, 657 (2002)CrossRefGoogle Scholar
  17. 17.
    V. Čápek, Eur. Phys. J. B 25, 101 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Institut für Theoretische Physik IUniversität StuttgartStuttgartGermany

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