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

• URL: http://arxiv.org/abs/2609.01606v1
• Date: Tue, 01 Sep 2026 17:59:58 GMT
• Title: Observable- and state-selective prethermalization and bounds on prethermal lifetimes
• Abstract summary: We show that a separation of spectral energy scales does not guarantee the appearance of a prethermal plateau.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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