English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We use the Toda chain model to demonstrate that numerical simulation ofintegrable Hamiltonian dynamics using time discretization destroysintegrability and induces dynamical chaos. Specifically, we integrate thismodel with various symplectic integrators parametrized by the time step $\tau$and measure the Lyapunov time $T_{\Lambda}$ (inverse of the largest Lyapunovexponent $\Lambda$). A key observation is that $T_{\Lambda}$ is finite whenever$\tau$ is finite but diverges when $\tau \rightarrow 0$. We compare the Todachain results with the nonitegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. Inaddition, we observe a breakdown of the simulations at times $T_B \ggT_{\Lambda}$ due to certain positions and momenta becoming extremely large(``Not a Number''). This phenomenon originates from the periodic drivingintroduced by symplectic integrators and we also identify the concretemechanism of the breakdown in the case of the Toda chain.

Dynamical chaos in the integrable Toda chain induced by time discretization