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Nonlinear Sciences > Chaotic Dynamics
Title: Effective stochastic model for chaos in the Fermi-Pasta-Ulam-Tsingou chain
(Submitted on 26 Jul 2021 (v1), last revised 10 Apr 2022 (this version, v2))
Abstract: Understanding the interplay between different wave excitations, such as phonons and localized solitons, is crucial for developing coarse-grained descriptions of many-body, near-integrable systems. We treat the Fermi-Pasta-Ulam-Tsingou (FPUT) non-linear chain and show numerically that at short timescales, relevant to the largest Lyapunov exponent, it can be modeled as a random perturbation of its integrable approximation -- the Toda chain. At low energies, the separation between two trajectories that start at close proximity is dictated by the interaction between few soliton modes and an intrinsic, apparent bath representing a background of many radiative modes. It is sufficient to consider only one randomly perturbed Toda soliton-like mode to explain the power-law profiles reported in previous works, describing how the Lyapunov exponent of large FPUT chains decreases with the energy density of the system.
Submission history
From: Tomer Goldfriend [view email][v1] Mon, 26 Jul 2021 21:32:32 GMT (929kb)
[v2] Sun, 10 Apr 2022 21:15:15 GMT (971kb)
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