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Random matrix universality in dynamical correlation functions at late times
by Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini
Submission summary
| Authors (as registered SciPost users): | Oscar Bouverot-Dupuis · Silvia Pappalardi · Anatoli Polkovnikov |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2407.12103v5 (pdf) |
| Date accepted: | July 14, 2025 |
| Date submitted: | July 10, 2025, 8:47 a.m. |
| Submitted by: | Oscar Bouverot-Dupuis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
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List of changes
Below we address the last questions of Referee 2.
\begin{enumerate}
\item[1] Yes with $e$ we mean the intensive energy $e = E/L $. The polynomial corrections we refer to concern indeed the two-point function.
We have corrected the typo in the text.
\item[2] Indeed differently from the SFF, $\Gamma$ is not positive defined so it can take negative values.
In the model we consider in the slope it shows a negative oscillation and then it goes back to be positive having a ramp and a plateau as we discuss.
\item[3] We agree that the analysis with dissipation would need a completely separate and dedicate work.
With this sentence we wanted just to give credit to some work which observed the noise is suppressed with dissipation.
Published as SciPost Phys. 19, 050 (2025)