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arXiv · 2602.23421

Integrability breaking in semiclassical strings in Koopman-Krylov space

Rathindra Nath Das·Saskia Demulder
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Abstract

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.

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Rathindra Nath Das, Saskia Demulder. 2026-02-26. Integrability breaking in semiclassical strings in Koopman-Krylov space. https://arxiv.org/abs/2602.23421

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