Random matrix universality in dynamical correlation functions at late times
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 correlation...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2025-08-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.2.050 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849233241891930112 |
|---|---|
| author | Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini |
| author_facet | Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini |
| author_sort | Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3236d9eec0fc40d79e2575c937f7ace7 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-3236d9eec0fc40d79e2575c937f7ace72025-08-20T09:15:35ZengSciPostSciPost Physics2542-46532025-08-0119205010.21468/SciPostPhys.19.2.050Random matrix universality in dynamical correlation functions at late timesOscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura FoiniWe 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.https://scipost.org/SciPostPhys.19.2.050 |
| spellingShingle | Oscar Bouverot-Dupuis, Silvia Pappalardi, Jorge Kurchan, Anatoli Polkovnikov, Laura Foini Random matrix universality in dynamical correlation functions at late times SciPost Physics |
| title | Random matrix universality in dynamical correlation functions at late times |
| title_full | Random matrix universality in dynamical correlation functions at late times |
| title_fullStr | Random matrix universality in dynamical correlation functions at late times |
| title_full_unstemmed | Random matrix universality in dynamical correlation functions at late times |
| title_short | Random matrix universality in dynamical correlation functions at late times |
| title_sort | random matrix universality in dynamical correlation functions at late times |
| url | https://scipost.org/SciPostPhys.19.2.050 |
| work_keys_str_mv | AT oscarbouverotdupuissilviapappalardijorgekurchananatolipolkovnikovlaurafoini randommatrixuniversalityindynamicalcorrelationfunctionsatlatetimes |