Quantum Chaos and Level Dynamics
We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving le...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/3/491 |
| _version_ | 1797611933264773120 |
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| author | Jakub Zakrzewski |
| author_facet | Jakub Zakrzewski |
| author_sort | Jakub Zakrzewski |
| collection | DOAJ |
| description | We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, such as level avoided-crossing distributions, level slope distributions, or level curvature distributions. We show both the aspects of universality in these distributions and their limitations. We concentrate in some detail on measures imported from the quantum information approach such as the fidelity susceptibility, and more generally, geometric tensor matrix elements. The possible open problems are suggested. |
| first_indexed | 2024-03-11T06:34:34Z |
| format | Article |
| id | doaj.art-0d439367cfcc4909a762d7fec65432df |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T06:34:34Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0d439367cfcc4909a762d7fec65432df2023-11-17T10:56:56ZengMDPI AGEntropy1099-43002023-03-0125349110.3390/e25030491Quantum Chaos and Level DynamicsJakub Zakrzewski0Institute of Theoretical Physics, Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, PolandWe review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, such as level avoided-crossing distributions, level slope distributions, or level curvature distributions. We show both the aspects of universality in these distributions and their limitations. We concentrate in some detail on measures imported from the quantum information approach such as the fidelity susceptibility, and more generally, geometric tensor matrix elements. The possible open problems are suggested.https://www.mdpi.com/1099-4300/25/3/49180th birthday of Giulio Casatiquantum chaoslevel dynamics |
| spellingShingle | Jakub Zakrzewski Quantum Chaos and Level Dynamics Entropy 80th birthday of Giulio Casati quantum chaos level dynamics |
| title | Quantum Chaos and Level Dynamics |
| title_full | Quantum Chaos and Level Dynamics |
| title_fullStr | Quantum Chaos and Level Dynamics |
| title_full_unstemmed | Quantum Chaos and Level Dynamics |
| title_short | Quantum Chaos and Level Dynamics |
| title_sort | quantum chaos and level dynamics |
| topic | 80th birthday of Giulio Casati quantum chaos level dynamics |
| url | https://www.mdpi.com/1099-4300/25/3/491 |
| work_keys_str_mv | AT jakubzakrzewski quantumchaosandleveldynamics |