Integrability breaking in semiclassical strings in Koopman-Krylov space

TL;DR

This paper introduces a Koopman-Krylov framework to analyze how integrability-breaking deformations affect the spectral properties and dynamics of semiclassical string solutions, providing new tools to characterize chaos in classical systems.

Contribution

The paper develops a novel Koopman-Krylov approach using gEDMD to study non-integrable string dynamics and spectral delocalization effects.

Findings

Spectral weight redistributes under integrability-breaking deformations.

Observable-dependent delocalization occurs in Krylov space.

Framework successfully applied to three classes of non-integrable strings.

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.