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Transport in perturbed classical integrable systems: The pinned Toda chain

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

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.

Suggested Citation

  • Di Cintio, Pierfrancesco & Iubini, Stefano & Lepri, Stefano & Livi, Roberto, 2018. "Transport in perturbed classical integrable systems: The pinned Toda chain," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 249-254.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:249-254
    DOI: 10.1016/j.chaos.2018.11.003
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    1. Livi, Roberto, 2023. "Anomalous transport in low-dimensional systems: A pedagogical overview," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 631(C).

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