Random matrix theory of integrability-to-chaos transition
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913058862923776 |
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| author | Craps, Ben De Clerck, Marine Evnin, Oleg Pavlov, Maxim |
| author_facet | Craps, Ben De Clerck, Marine Evnin, Oleg Pavlov, Maxim |
| contents | The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and described by the Poisson vs. Wigner-Dyson curves. In the transitional regime between integrability and chaos, the distributions are much less universal and have not been understood quantitatively until now. We point out that the relevant statistics that controls these distributions is that of the matrix elements of the nonintegrable perturbation Hamiltonian in the energy eigenbasis of the unperturbed integrable system. With this insight, we formulate a simple random matrix ensemble that correctly reproduces the level spacing distributions in a variety of test systems. For the distribution of matrix elements appearing in our construction, we furthermore discover surprising universal features: across a variety of physical systems with diverse degrees of freedom, these distributions are dominated by simple power laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random matrix theory of integrability-to-chaos transition Craps, Ben De Clerck, Marine Evnin, Oleg Pavlov, Maxim Statistical Mechanics Mathematical Physics Chaotic Dynamics Quantum Physics The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and described by the Poisson vs. Wigner-Dyson curves. In the transitional regime between integrability and chaos, the distributions are much less universal and have not been understood quantitatively until now. We point out that the relevant statistics that controls these distributions is that of the matrix elements of the nonintegrable perturbation Hamiltonian in the energy eigenbasis of the unperturbed integrable system. With this insight, we formulate a simple random matrix ensemble that correctly reproduces the level spacing distributions in a variety of test systems. For the distribution of matrix elements appearing in our construction, we furthermore discover surprising universal features: across a variety of physical systems with diverse degrees of freedom, these distributions are dominated by simple power laws. |
| title | Random matrix theory of integrability-to-chaos transition |
| topic | Statistical Mechanics Mathematical Physics Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2604.03669 |