Transport in perturbed classical integrable systems: the pinned Toda chain

Pierfrancesco Di Cintio; Stefano Iubini; Stefano Lepri; Roberto Livi

doi:10.1016/j.chaos.2018.11.003

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arXiv · 1810.07127

Transport in perturbed classical integrable systems: the pinned Toda chain

Pierfrancesco Di Cintio·Stefano Iubini·Stefano Lepri·Roberto Livi

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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.

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physics.plasm-ph cond-mat.stat-mech math-ph math.MP nlin.PS

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Pierfrancesco Di Cintio, Stefano Iubini, Stefano Lepri, Roberto Livi. 2018-10-16. Transport in perturbed classical integrable systems: the pinned Toda chain. https://doi.org/10.1016/j.chaos.2018.11.003

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