Transport in perturbed classical integrable systems: The pinned Toda chain

Pierfrancesco Di Cintio, Stefano Iubini, Stefano Lepri and Roberto Livi

Chaos, Solitons & Fractals, 2018, vol. 117, issue C, 249-254

Abstract: Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [ArXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by computing the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.

Keywords: Thermal transport; Integrability; Non-linearity; Lyapunov spectra (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:117:y:2018:i:c:p:249-254

DOI: 10.1016/j.chaos.2018.11.003

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