Krylov complexity as a probe for chaos
Abstract In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner in which complexity saturates reveals the chaotic...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-14451-z |
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| author | Mohsen Alishahiha Souvik Banerjee Mohammad Javad Vasli |
| author_facet | Mohsen Alishahiha Souvik Banerjee Mohammad Javad Vasli |
| author_sort | Mohsen Alishahiha |
| collection | DOAJ |
| description | Abstract In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner in which complexity saturates reveals the chaotic nature of the system. In particular, we show that the dynamics towards saturation precisely distinguish between chaotic and integrable systems. For chaotic models, the saturation value of complexity reaches its infinite time average at a finite saturation time. In this case, depending on the initial state, it may also exhibit a peak before saturation. In contrast, in integrable models, complexity approaches the infinite time average value from below at a much longer timescale. We confirm this distinction using numerical results for specific spin models. |
| format | Article |
| id | doaj-art-a686ec05901f45eb86f0286a865988e6 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-a686ec05901f45eb86f0286a865988e62025-08-20T04:03:06ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-07-0185711110.1140/epjc/s10052-025-14451-zKrylov complexity as a probe for chaosMohsen Alishahiha0Souvik Banerjee1Mohammad Javad Vasli2School of Physics, Institute for Research in Fundamental Sciences (IPM)Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität WürzburgSchool of Physics, Institute for Research in Fundamental Sciences (IPM)Abstract In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner in which complexity saturates reveals the chaotic nature of the system. In particular, we show that the dynamics towards saturation precisely distinguish between chaotic and integrable systems. For chaotic models, the saturation value of complexity reaches its infinite time average at a finite saturation time. In this case, depending on the initial state, it may also exhibit a peak before saturation. In contrast, in integrable models, complexity approaches the infinite time average value from below at a much longer timescale. We confirm this distinction using numerical results for specific spin models.https://doi.org/10.1140/epjc/s10052-025-14451-z |
| spellingShingle | Mohsen Alishahiha Souvik Banerjee Mohammad Javad Vasli Krylov complexity as a probe for chaos European Physical Journal C: Particles and Fields |
| title | Krylov complexity as a probe for chaos |
| title_full | Krylov complexity as a probe for chaos |
| title_fullStr | Krylov complexity as a probe for chaos |
| title_full_unstemmed | Krylov complexity as a probe for chaos |
| title_short | Krylov complexity as a probe for chaos |
| title_sort | krylov complexity as a probe for chaos |
| url | https://doi.org/10.1140/epjc/s10052-025-14451-z |
| work_keys_str_mv | AT mohsenalishahiha krylovcomplexityasaprobeforchaos AT souvikbanerjee krylovcomplexityasaprobeforchaos AT mohammadjavadvasli krylovcomplexityasaprobeforchaos |