Transport in perturbed classical integrable systems: The pinned Toda chain. (December 2018)

• Record Type: Journal Article
• Authors: Di Cintio, Pierfrancesco; Iubini, Stefano; Lepri, Stefano; Livi, Roberto
• Is Part Of: Chaos, solitons and fractals. Volume 117(2018)
• Page Start: 249
• Page End: 254
• Publication Date: 2018-12
• Subjects: Thermal transport -- Integrability -- Non-linearity -- Lyapunov spectra; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.11.003
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Spreading of localized perturbations in non-linear lattices. Ballistic transport in integrable models. Lyapunov spectra of perturbed integrable Hamiltonians. Anomalous transport in low dimensional systems. 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.