Krylov Complexity in Mixed Phase Space
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913899603820544 |
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| author | Huh, Kyoung-Bum Jeong, Hyun-Sik Zayas, Leopoldo A. Pando Pedraza, Juan F. |
| author_facet | Huh, Kyoung-Bum Jeong, Hyun-Sik Zayas, Leopoldo A. Pando Pedraza, Juan F. |
| contents | We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Krylov Complexity in Mixed Phase Space Huh, Kyoung-Bum Jeong, Hyun-Sik Zayas, Leopoldo A. Pando Pedraza, Juan F. High Energy Physics - Theory Chaotic Dynamics Quantum Physics We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems. |
| title | Krylov Complexity in Mixed Phase Space |
| topic | High Energy Physics - Theory Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2412.04963 |