Temporal correlations and chaos from spacetime kernel
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908695381671936 |
|---|---|
| author | Das, Rathindra Nath Kundu, Arnab Costa, Matheus H. Martins Sarkar, Nemai Chandra |
| author_facet | Das, Rathindra Nath Kundu, Arnab Costa, Matheus H. Martins Sarkar, Nemai Chandra |
| contents | We develop a finite-dimensional formulation of the recently introduced notion of ``timelike entanglement'', defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator basis, we recast this construction in terms of a generalized response tensor. Building on this, we introduce a generalized spacetime density kernel (GSDK) corresponding to higher-point correlation functions, including time-ordered as well as out-of-time-ordered correlators. We show that the Haar-averaged $(2N)$-point function yields the $(2N)$-th moment of the spectral form factor (SFF), evaluated at an $N$-enhanced effective temperature. The correlation functions of the GSDK operators also yield the SFF, with an effective $(1/N)$-reduction of the physical time-scales. The GSDK places both scrambling diagnostics and spectral statistics on a similar footing and clarifies how higher-point correlators and non-trivial time ordering capture fine-grained dynamical information of a quantum system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Temporal correlations and chaos from spacetime kernel Das, Rathindra Nath Kundu, Arnab Costa, Matheus H. Martins Sarkar, Nemai Chandra High Energy Physics - Theory Quantum Physics We develop a finite-dimensional formulation of the recently introduced notion of ``timelike entanglement'', defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator basis, we recast this construction in terms of a generalized response tensor. Building on this, we introduce a generalized spacetime density kernel (GSDK) corresponding to higher-point correlation functions, including time-ordered as well as out-of-time-ordered correlators. We show that the Haar-averaged $(2N)$-point function yields the $(2N)$-th moment of the spectral form factor (SFF), evaluated at an $N$-enhanced effective temperature. The correlation functions of the GSDK operators also yield the SFF, with an effective $(1/N)$-reduction of the physical time-scales. The GSDK places both scrambling diagnostics and spectral statistics on a similar footing and clarifies how higher-point correlators and non-trivial time ordering capture fine-grained dynamical information of a quantum system. |
| title | Temporal correlations and chaos from spacetime kernel |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2512.06078 |