TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.4.136
TI  - Out-of-equilibrium eigenstate thermalization hypothesis
PY  - 2025/04/24
UR  - https://scipost.org/SciPostPhys.18.4.136
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 4
SP  - 136
A1  - Foini, Laura
AU  - Dymarsky, Anatoly
AU  - Pappalardi, Silvia
AB  - 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, in order to describe such evolution. The approach is inspired by the Eigenstate Thermalisation Hypothesis (ETH) but the proposed Ansatz exhibits different scaling. Importantly, we point out the exponentially small cross-correlations between the observable and the initial state matrix elements that 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.
ER  -

@Article{10.21468/SciPostPhys.18.4.136,
	title={{Out-of-equilibrium eigenstate thermalization hypothesis}},
	author={Laura Foini and Anatoly Dymarsky and Silvia Pappalardi},
	journal={SciPost Phys.},
	volume={18},
	pages={136},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.4.136},
	url={https://scipost.org/10.21468/SciPostPhys.18.4.136},
}