Random matrix universality in dynamical correlation functions at late times
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913996771164160 |
|---|---|
| author | Bouverot-Dupuis, Oscar Pappalardi, Silvia Kurchan, Jorge Polkovnikov, Anatoli Foini, Laura |
| author_facet | Bouverot-Dupuis, Oscar Pappalardi, Silvia Kurchan, Jorge Polkovnikov, Anatoli Foini, Laura |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random matrix universality in dynamical correlation functions at late times Bouverot-Dupuis, Oscar Pappalardi, Silvia Kurchan, Jorge Polkovnikov, Anatoli Foini, Laura Statistical Mechanics High Energy Physics - Theory 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. |
| title | Random matrix universality in dynamical correlation functions at late times |
| topic | Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.12103 |