Integrability breaking in semiclassical strings in Koopman-Krylov space
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914355536199680 |
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| author | Das, Rathindra Nath Demulder, Saskia |
| author_facet | Das, Rathindra Nath Demulder, Saskia |
| contents | While very powerful, integrability in semiclassical string solutions is known to be a rare property. Motivated by the need to understand and characterise the large landscape of non-integrable string dynamics, we extend Krylov methods for probing chaos to classical systems. We introduce a Koopman-Krylov framework, formulated in the Koopman-von Neumann description of classical mechanics and implemented via a generator extended dynamic mode decomposition (gEDMD) approximation of the Koopman generator acting on observables. Using this framework, we study how integrability-breaking deformations of integrable string dynamics induce characteristic redistributions of spectral weight, leading to observable-dependent delocalisation and spreading in Krylov space. We illustrate the Koopman-Krylov diagnostics across three classes of non-integrable semiclassical string solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrability breaking in semiclassical strings in Koopman-Krylov space Das, Rathindra Nath Demulder, Saskia High Energy Physics - Theory Chaotic Dynamics Quantum Physics While very powerful, integrability in semiclassical string solutions is known to be a rare property. Motivated by the need to understand and characterise the large landscape of non-integrable string dynamics, we extend Krylov methods for probing chaos to classical systems. We introduce a Koopman-Krylov framework, formulated in the Koopman-von Neumann description of classical mechanics and implemented via a generator extended dynamic mode decomposition (gEDMD) approximation of the Koopman generator acting on observables. Using this framework, we study how integrability-breaking deformations of integrable string dynamics induce characteristic redistributions of spectral weight, leading to observable-dependent delocalisation and spreading in Krylov space. We illustrate the Koopman-Krylov diagnostics across three classes of non-integrable semiclassical string solutions. |
| title | Integrability breaking in semiclassical strings in Koopman-Krylov space |
| topic | High Energy Physics - Theory Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2602.23421 |