Prethermalization and relaxation rates of observables in isolated quantum systems

Tim Langen, Jörg Schmiedmayer

Takashi Mori, Tatsuhiko N. Ikeda, Eriko Kaminishi +1 more

Abstract The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal testbed to study the nonequilibrium dynamics in isolated quantum systems, promoting intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation of relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

Madhukar Mallayya Krishnanand

Zhe-Xuan Gong, L-M Duan

We propose an experimental scheme to observe prethermalization and a dynamic phase transition in a one-dimensional XY spin chain with long-range interactions and inhomogeneous lattice spacing, which can be readily implemented with a recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at an intermediate timescale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is shown to result from a non-trivial structure in the lower half of the energy spectrum. The dynamic behavior of the system is shown to cross different phases when the interaction range is continuously tuned, indicating the existence of a dynamic phase transition.

Osamu Fukushima

Jakub Pawłowski, Miłosz Panfil, J. Herbrych +1 more

Relaxation rates in nearly integrable systems usually increase quadratically with the strength of the perturbation that breaks integrability. We show that the relaxation rates can be significantly smaller in systems that are integrable along two intersecting lines in the parameter space. In the vicinity of the intersection point, the relaxation rates of certain observables increase with the fourth power of the distance from this point, whereas for other observables one observes standard quadratic dependence on the perturbation. As a result, one obtains exceedingly long-living prethermalization but with a reduced number of the nearly conserved operators. We show also that such a scenario can be realized in spin ladders.