Universal law of thermalization for one-dimensional perturbed Toda lattices

Abstract

The Toda lattice is a nonlinear but integrable system. Here we study the thermalization problem in one-dimensional, perturbed Toda lattices in the thermodynamic limit. We show that the thermalization time, T _eq , follows a universal law; i.e. T _eq ∼ ϵ ^−2 , where the perturbation strength , ϵ , characterizes the nonlinear perturbations added to the Toda potential. This universal law applies generally to weak nonlinear lattices due to their equivalence to perturbed Toda systems.

Keywords

• Fermi–Pasta–Ulam–Tsingou problem
• anharmonic chains
• energy equipartition