TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.2.050
TI  - Random matrix universality in dynamical correlation functions at late times
PY  - 2025/08/20
UR  - https://www.scipost.org/SciPostPhys.19.2.050
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 2
SP  - 050
A1  - Bouverot-Dupuis, Oscar
AU  - Pappalardi, Silvia
AU  - Kurchan, Jorge
AU  - Polkovnikov, Anatoli
AU  - Foini, Laura
AB  - We study the behaviour of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions display a ramp and a plateau determined by the correlations of energy levels, similar to what is already known for the spectral form factor. The plateau value is determined, in absence of degenerate energy levels, by the fluctuations of diagonal matrix elements, which highlights differences between different symmetry classes. We show this behaviour analytically by employing results from Random Matrix Theory and the Eigenstate Thermalisation Hypothesis, and numerically by exact diagonalization in the toy example of a Hamiltonian drawn from a Random Matrix ensemble and in a more realistic example of disordered spin glasses at high temperature. Importantly, correlation functions in the ramp regime do not show self-averaging behaviour, and, at difference with the spectral form factor the time average does not coincide with the ensemble average.
ER  -

@Article{10.21468/SciPostPhys.19.2.050,
	title={{Random matrix universality in dynamical correlation functions at late times}},
	author={Oscar Bouverot-Dupuis and Silvia Pappalardi and Jorge Kurchan and Anatoli Polkovnikov and Laura Foini},
	journal={SciPost Phys.},
	volume={19},
	pages={050},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.2.050},
	url={https://scipost.org/10.21468/SciPostPhys.19.2.050},
}