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Lanczos spectrum for random operator growth
by Tran Quang Loc
Submission summary
| Authors (as registered SciPost users): | Quang Loc Tran |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2402.07980v2 (pdf) |
| Date submitted: | 2024-03-21 08:43 |
| Submitted by: | Tran, Quang Loc |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Current status:
In refereeing