Out-of-equilibrium Eigenstate Thermalization Hypothesis
- URL: http://arxiv.org/abs/2406.04684v2
- Date: Wed, 3 Jul 2024 07:20:49 GMT
- Title: Out-of-equilibrium Eigenstate Thermalization Hypothesis
- Authors: Laura Foini, Anatoly Dymarsky, Silvia Pappalardi,
- Abstract summary: We show that universality, exponentially small cross-correlations between the observable and the initial state matrix elements determine relaxation dynamics toward equilibrium.
We numerically verify scaling and cross-correlation, point out the emergent of the high-frequency behavior, and outline possible generalizations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Understanding how out-of-equilibrium states thermalize under quantum unitary dynamics is an important problem in many-body physics. In this work, we propose a statistical ansatz for the matrix elements of non-equilibrium initial states in the energy eigenbasis. The approach is inspired by the Eigenstate Thermalisation Hypothesis (ETH) but the proposed ansatz exhibits different scaling. Importantly, exponentially small cross-correlations between the observable and the initial state matrix elements determine relaxation dynamics toward equilibrium. We numerically verify scaling and cross-correlation, point out the emergent universality of the high-frequency behavior, and outline possible generalizations.
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