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  • Open Access

Adiabatic gauge potential as a tool for detecting chaos in classical systems

Nachiket Karve*, Nathan Rose, and David Campbell

  • *Contact author: nachiket@bu.edu
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Phys. Rev. Research 7, 033006 – Published 1 July, 2025

DOI: https://doi.org/10.1103/1z5x-j644

Abstract

The interplay between chaos and thermalization in weakly nonintegrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical systems. In this work, we study the adiabatic gauge potential (AGP), an object typically studied in quantum mechanics that describes deformations of a quantum state under adiabatic variation of the Hamiltonian, in classical Fermi-Pasta-Ulam-Tsingou (FPUT) and Toda models. We show how the time variance of the AGP over a trajectory probes the longtime correlations of a generic observable and can be used to distinguish among nearly integrable, weakly chaotic, and strongly chaotic regimes. We draw connections between the evolution of the AGP and diffusion and derive a fluctuation-dissipation relation that connects its variance to longtime correlations of the observable. Within this framework, we demonstrate that strongly and weakly chaotic regimes correspond to normal and anomalous diffusion, respectively. The latter gives rise to a marked increase in the variance as the time interval is increased, and this behavior serves as the basis for our probe of the onset times of chaos, which is interpreted as a “mixing” time. Numerical results are presented for FPUT and Toda systems that highlight integrable, weakly chaotic, and strongly chaotic regimes. Further, a hierarchy of tLyapunov<tchaos<tthermalization is found in these models. We conclude by commenting on the wide applicability of our method to a broader class of systems.

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Phys. Rev. Research 7, 033006– Published 1 July, 2025
  • Received 17 February 2025
  • Accepted 21 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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