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Dynamical chaos in the integrable Toda chain induced by time discretization

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Title
Dynamical chaos in the integrable Toda chain induced by time discretization
Author(s)
Danieli, Carlo; Yuzbashyan, Emil A.; Altshuler, Boris L.; Aniket Patra; Sergej Flach
Publication Date
2024-03
Journal
Chaos, v.34, no.3
Publisher
American Institute of Physics
Abstract
We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step τ and measure the Lyapunov time T Λ (inverse of the largest Lyapunov exponent Λ ). A key observation is that T Λ is finite whenever τ is finite but diverges when τ → 0 . We compare the Toda chain results with the nonintegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times T B ≫ T Λ due to certain positions and momenta becoming extremely large (“Not a Number”). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain. © 2024 Author(s).
URI
https://pr.ibs.re.kr/handle/8788114/15072
DOI
10.1063/5.0171261
ISSN
1054-1500
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > 1. Journal Papers (저널논문)
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