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 studies^{1, 2} of the problem have become possible, stimulating theoretical interest^{3, 4, 5, 6, 7}. In generic isolated systems, non-equilibrium dynamics is expected^{8, 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 studies^{4, 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.