Article Dans Une Revue SciPost Physics Année : 2025

Random matrix universality in dynamical correlation functions at late times

Résumé

We study the behavior 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 behavior 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.

Fichier principal
Vignette du fichier
SciPostPhys_19_2_050.pdf (572.41 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Licence

Dates et versions

hal-04661833 , version 1 (26-08-2025)

Licence

Identifiants

Citer

Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini. Random matrix universality in dynamical correlation functions at late times. SciPost Physics, 2025, 19 (2), pp.050. ⟨10.21468/SciPostPhys.19.2.050⟩. ⟨hal-04661833⟩
406 Consultations
144 Téléchargements

Altmetric

Partager

  • More