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 17.04.2008   Карта сайта     Language По-русски По-английски
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17.04.2008

Letter


Nature 452, 854-858 (17 April 2008) | doi:10.1038/nature06838; Received 7 December 2007; Accepted 13 February 2008



Thermalization and its mechanism for generic isolated quantum systems


Marcos Rigol1,2, Vanja Dunjko1,2 & Maxim Olshanii2




  1. Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
  2. Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA


Correspondence to: Maxim Olshanii2 Correspondence and requests for materials should be addressed to M.O. (Email: maxim.olchanyi@umb.edu).





An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies1, 2 of the problem have become possible, stimulating theoretical interest3, 4, 5, 6, 7. In generic isolated systems, non-equilibrium dynamics is expected8, 9 to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible10. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete11. Some recent studies4, 5 even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems. Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch12 and Srednicki13. A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result.



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  • Chen Wev .  honorary member of ISSC science council

  • Harton Vladislav Vadim  honorary member of ISSC science council

  • Lichtenstain Alexandr Iosif  honorary member of ISSC science council

  • Novikov Dimirtii Leonid  honorary member of ISSC science council

  • Yakushev Mikhail Vasilii  honorary member of ISSC science council

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