Universal law of thermalization for one-dimensional perturbed Toda lattices

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, Teq, follows a universal law; i.e. Teq ∼ ϵ−2, where the perturbation strength, ϵ, characterize...

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Bibliographic Details
Published in:New journal of physics 2019-04, Vol.21 (4), p.43009
Main Authors: Fu, Weicheng, Zhang, Yong, Zhao, Hong
Format: Article
Language:English
Subjects:
anharmonic chains
energy equipartition
Fermi-Pasta-Ulam-Tsingou problem
Lattices
Perturbation
Physics
Thermalization (energy absorption)
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Summary: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, Teq, follows a universal law; i.e. Teq ∼ 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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ab115a