Towards local equilibration in closed interacting quantum many-body systems

TL;DR

This paper discusses why local expectation values in generic interacting quantum many-body systems tend to equilibrate quickly, emphasizing intuitive explanations, connecting to existing theories, and supporting with numerical examples.

Contribution

It provides simple, plausible arguments for the mechanisms behind local equilibration in interacting quantum systems, clarifying underlying principles without rigorous proofs.

Findings

Empirical evidence suggests local observables equilibrate independently of system size.

Numerical results support the plausibility of rapid local equilibration.

Connections made to eigenstate thermalization hypothesis and rigorous results.

Abstract

One of the main questions of research on quantum many-body systems following unitary out of equilibrium dynamics is to find out how local expectation values equilibrate in time. For non-interacting models, this question is rather well understood. However, the best known bounds for general quantum systems are vastly crude, scaling unfavorable with the system size. Nevertheless, empirical and numerical evidence suggests that for generic interacting many-body systems, generic local observables, and sufficiently well-behaved states, the equilibration time does not depend strongly on the system size, but only the precision with which this occurs does. In this discussion paper, we aim at giving very simple and plausible arguments for why this happens. While our discussion does not yield rigorous results about equilibration time scales, we believe that it helps to clarify the essential underlying mechanisms, the intuition and important figure of merits behind equilibration. We then connect our arguments to common assumptions and numerical results in the field of equilibration and thermalization of closed quantum systems, such as the eigenstate thermalization hypothesis as well as rigorous results on interacting quantum many-body systems. Finally, we complement our discussions with numerical results - both in the case of examples and counter-examples of equilibrating systems.