TY - JOUR

T1 - Thermalization and its mechanism for generic isolated quantum systems

AU - Rigol, Marcos

AU - Dunjko, Vanja

AU - Olshanii, Maxim

N1 - Funding Information:
Acknowledgements We thank A. C. Cassidy, K. Jacobs, A. P. Young, and E. J. Heller for their comments. We acknowledge financial support from the National Science Foundation and the Office of Naval Research. We are grateful to the USC HPCC centre, where all our numerical computations were performed.

PY - 2008/4/17

Y1 - 2008/4/17

N2 - An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies of the problem have become possible, stimulating theoretical interest. In generic isolated systems, non-equilibrium dynamics is expected 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 possible. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete. Some recent studies 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 Deutsch and Srednicki. 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.

AB - An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies of the problem have become possible, stimulating theoretical interest. In generic isolated systems, non-equilibrium dynamics is expected 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 possible. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete. Some recent studies 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 Deutsch and Srednicki. 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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U2 - 10.1038/nature06838

DO - 10.1038/nature06838

M3 - Article

C2 - 18421349

AN - SCOPUS:42249112261

VL - 452

SP - 854

EP - 858

JO - Nature

JF - Nature

SN - 0028-0836

IS - 7189

ER -