Lanczos spectrum for random operator growth
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914711267704832 |
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| author | Loc, Tran Quang |
| author_facet | Loc, Tran Quang |
| contents | Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the context of Schrodinger evolution, this tridiagonalization has been carried out in Random Matrix Theory. We extend these developments to Heisenberg time evolution, describing how the Liouvillian can be tridiagonalized as well until the end of Krylov space. We numerically verify the analytical formulas both for Gaussian and non-Gaussian matrix models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lanczos spectrum for random operator growth Loc, Tran Quang High Energy Physics - Theory Statistical Mechanics Mathematical Physics Chaotic Dynamics Quantum Physics Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the context of Schrodinger evolution, this tridiagonalization has been carried out in Random Matrix Theory. We extend these developments to Heisenberg time evolution, describing how the Liouvillian can be tridiagonalized as well until the end of Krylov space. We numerically verify the analytical formulas both for Gaussian and non-Gaussian matrix models. |
| title | Lanczos spectrum for random operator growth |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2402.07980 |