2007/08/31 by Marcos Rigol, Vanja Dunjko, Maxim Olshanii · 3,139 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Eigenvalues and eigenvectors #Observable #Physics #Quantum #Quantum chaos #Quantum dynamics #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum statistical mechanics #Quantum system #Relaxation (psychology) #Spectroscopy and Quantum Chemical Studies #Statistical mechanics #Statistical physics #Theoretical physics #Thermalisation #Time evolution #cond-mat.stat-mech
paper · pdf · doi:10.1038/nature06838
published in Nature 452(7189), 854-858 (Nature Portfolio) · 8 pages, 6 figures, as published
openalex publication_date 2008/04/16 · arxiv created 2009/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in this field is perhaps most urgently needed in the foundations of quantum statistical mechanics. This is so because in generic isolated systems, one expects nonequilibrium dynamics on its own to result in thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of 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, where time evolution is linear and the spectrum is discrete. Underscoring that new rules could apply in this case, some recent studies even suggested that statistical mechanics may give wrong predictions for the outcomes of relaxation in such systems. Here we demonstrate that an isolated generic quantum many-body system does in fact 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 happens instead at the level of individual eigenstates, as first proposed by J.M. Deutsch and M. Srednicki. A striking consequence of this eigenstate thermalization scenario is that the knowledge of a single many-body eigenstate suffices to compute thermal averages-any eigenstate in the microcanonical energy window will do, as they all give the same result.