Journal Article

Thermalization and its mechanism for generic isolated quantum systems

Olshanii, Maxim, Rigol, Marcos, Dunjko, Vanja

2008

Overview

It is demonstrated that an isolated generic quantum many-body system does relax to a state well described by the standard statistical mechanical prescription. The thermalization happens at the level of individual eigenstates, allowing the computation of thermal averages from knowledge of any eigenstate in the microcanonical energy window. 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 possible 10 . For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete 11 . 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 Deutsch 12 and Srednicki 13 . 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.

• Publisher: Nature Publishing Group UK,Nature Publishing,Nature Publishing Group
• Subject: Chaos theory / Eigenvalues / Exact sciences and technology / Humanities and Social Sciences / letter / multidisciplinary / Nonlinear dynamics and nonlinear dynamical systems / Physics / Quantum theory / Science / Science (multidisciplinary) / Statistical physics, thermodynamics, and nonlinear dynamical systems / Thermodynamics / Time