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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.16669 |
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| _version_ | 1866914645582807040 |
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| author | Hashimoto, Koji Murata, Keiju Tanahashi, Norihiro Watanabe, Ryota |
| author_facet | Hashimoto, Koji Murata, Keiju Tanahashi, Norihiro Watanabe, Ryota |
| contents | Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16669 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Krylov complexity and chaos in quantum mechanics Hashimoto, Koji Murata, Keiju Tanahashi, Norihiro Watanabe, Ryota High Energy Physics - Theory Chaotic Dynamics Quantum Physics Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos. |
| title | Krylov complexity and chaos in quantum mechanics |
| topic | High Energy Physics - Theory Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2305.16669 |