We discuss the approach toward equilibrium of an isolated quantum system. For a wide class of systems, in particular, for chaotic systems, we argue that the expectation value of a local operator averaged over a time interval of length T is bounded by the so-called deviation function, which characterizes maximal deviation from the equilibrium of all states with a given value of energy fluctuations. This result applies to any initial state with a well-defined effective temperature. We provide numerical evidence that the bound is approximately saturated by the initial configurations with spatial inhomogeneities at a macroscopic level. In this way the deviation function establishes an explicit connection between the macroscopically observed timescales associated with the transport and the properties of microscopic matrix elements. The form of the deviation function indicates that among the "slowest" states which saturate the bound there are also those with arbitrarily long equilibration times.
|Physical Review B
|Published - Jun 6 2019
Bibliographical noteFunding Information:
I am grateful to Joel Lebowitz and David Huse for helpful discussions. I would also like to thank Tomaz Prosen, Hong Liu, Moshe Rozali, and Luis Pedro Garcia-Pintos for reading the manuscript and helpful comments. I acknowledge the University of Kentucky Center for Computational Sciences for computing time on the Lipscomb High Performance Computing Cluster. This work was supported by a grant of the Russian Science Foundation (Project No. 17-12-01587).
© 2019 American Physical Society.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics