Non-Equilibrium Dynamics and Weakly Broken Integrability

Abstract

Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model we establish an analytical approach to real-time dynamics. The method addresses a broad range of timescales, from the intermediate regime of pre-thermalization to late-time thermalization. Predictions are given for the time-evolution of physical quantities, including effective temperatures and thermalization rates. The approach provides conceptual links between perturbed quantum many-body dynamics and classical Kolmogorov-Arnold-Moser (KAM) theory. In particular, we identify a family of perturbations which do not cause thermalization in the weakly perturbed regime.

v4: Improved discussion of perturbed Lieb-Liniger model and interactions. 5+10 pages, 3+7 figures. v3: New discussion of perturbed Lieb-Liniger model, mentioned in text and new section in SM. 5+10 pages, 3+7 figures. v2: references added and discussion of nearly-integrable perturbations improved. 5+9 pages, 3+5 figures