Statistics of local level spacings in single- and many-body quantum chaos
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917678745124864 |
|---|---|
| author | Tian, Peng Riser, Roman Kanzieper, Eugene |
| author_facet | Tian, Peng Riser, Roman Kanzieper, Eugene |
| contents | We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal -- chaotic or regular -- dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards and many-body spectra of the Sachdev-Ye-Kitaev Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06766 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Statistics of local level spacings in single- and many-body quantum chaos Tian, Peng Riser, Roman Kanzieper, Eugene Mathematical Physics Disordered Systems and Neural Networks High Energy Physics - Theory Exactly Solvable and Integrable Systems Quantum Physics We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal -- chaotic or regular -- dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards and many-body spectra of the Sachdev-Ye-Kitaev Hamiltonians. |
| title | Statistics of local level spacings in single- and many-body quantum chaos |
| topic | Mathematical Physics Disordered Systems and Neural Networks High Energy Physics - Theory Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2308.06766 |