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A quantum many-body system which is prepared in the ground state of anintegrable Hamiltonian does not directly thermalize after a sudden smallparameter quench away from integrability. Rather, it will be trapped in aprethermalized state and can thermalize only at a later stage. We discussseveral examples for which this prethermalized state shares some propertieswith the nonthermal steady state that emerges in the corresponding integrablesystem. These examples support the notion that nonthermal steady states inintegrable systems may be viewed as prethermalized states that never decayfurther. Furthermore we show that prethermalization plateaus are under certainconditions correctly predicted by generalized Gibbs ensembles, which are theappropriate extension of standard statistical mechanics in the presence of manyconstants of motion. This establishes that the relaxation behaviors ofintegrable and nearly integrable systems are continuously connected anddescribed by the same statistical theory.

Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems