Transport in perturbed classical integrable systems: the pinned Toda chain

TL;DR

This paper investigates how adding nonintegrable perturbations to the Toda chain affects its transport properties, revealing non-integrability, diffusive conductivity, and unique dynamical features like soliton-like excitations.

Contribution

It demonstrates that even quadratic pinning makes the Toda chain non-integrable and explores the resulting transport and dynamical behaviors through simulations.

Findings

Quadratic pinning induces non-integrability in the Toda chain.

The system exhibits normal diffusive conductivity for long chains.

Soliton-like excitations influence transport and correlation decay.

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.