Universal law of thermalization for one-dimensional perturbed Toda lattices

Weicheng Fu, Yong Zhang, Hong Zhao
2019 New Journal of Physics  
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.
doi:10.1088/1367-2630/ab115a fatcat:rifiljfhjjg4nf5owcfvvhcl54