Observable- and state-selective prethermalization and bounds on prethermal lifetimes

Abstract:Prethermalization describes long-lived intermediate regimes that precede equilibrium and can dominate experimentally accessible dynamics. Here, we show that a separation of spectral energy scales, despite giving rise to a hierarchy of dynamical timescales, does not by itself guarantee the appearance of a prethermal plateau. Under the same Hamiltonian, some observables may exhibit prethermal behavior, while others relax directly toward equilibrium. We uncover the mechanism governing this selectivity, showing that the emergence of a prethermal plateau depends not only on the Hamiltonian, but also on the observable and the initial state. Our results apply broadly to systems close to a fully permutation-symmetric limit and are illustrated with a long-range interacting spin model. We further prove that the Loschmidt echo provides a lower bound on the prethermal lifetime of any bounded observable whenever the prethermal and exact dynamics are unitary.

12 pages, 4 figures; This manuscript presents the dynamical part of the work originally posted on arXiv as [arXiv.2607.15350v1], which has since been split into two papers. That arXiv manuscript now contains only the static part

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.01606 [quant-ph]

(or arXiv:2609.01606v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.01606 arXiv-issued DOI via DataCite (pending registration)