Articolo in rivista, 2018, ENG, 10.1016/j.chaos.2018.11.003

Transport in perturbed classical integrable systems: The pinned Toda chain

Di Cintio P.; Iubini S.; Lepri S.; Livi R.

Consiglio Nazionale delle Ricerche, Istituto di Fisica Applicata "Nello Carrara", via Madonna del piano 10, Sesto Fiorentino, I-50019, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, Sesto Fiorentino, I-50019, Italy; Dipartimento di Fisica e Astronomia, Università di Padova, via F. Marzolo 8, Padova, I-35131, Italy; Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, Sesto Fiorentino, I-50019, Italy; Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, Sesto Fiorentino, I-50019, Italy

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.

Chaos, solitons and fractals 117 , pp. 249–254

Keywords

Integrability, Lyapunov spectra, Non-linearity, Thermal transport

CNR authors

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

CNR institutes

IFAC – Istituto di fisica applicata "Nello Carrara", ISC – Istituto dei sistemi complessi