2018/10/16 by Pierfrancesco Di Cintio, Stefano Iubini, Stefano Lepri +1 · 28 citations
Materials Science · Mathematics · Physics and Astronomy · #Chain (unit) #Classical mechanics #Geometry #Integrable system #Lattice (music) #Lyapunov exponent #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Nonlinear system #Physics #Quadratic equation #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Thermal properties of materials #Toda lattice #cond-mat.stat-mech #math-ph #math.MP #nlin.PS #physics.plasm-ph
paper · pdf · doi:10.1016/j.chaos.2018.11.003
published in Chaos Solitons & Fractals 117, 249-254 (Elsevier BV) · 8 pages, 6 figures. Submitted to CSF, comments welcome
arxiv created 2018/10/16 · openalex publication_date 2018/11/09 · arxiv updated 2018/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.