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., $T_{eq}\sim {\epsilon }^{-2}$, where the perturbation strength, $\epsilon$, 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.

References in corpus (16)

• The Fermi-Pasta-Ulam problem: 50 years of progress
• Fermi, Pasta, Ulam and a mysterious lady
• Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather Solitons in an Optical Microresonator
• A route to thermalization in the $\alpha$-Fermi-Pasta-Ulam system
• q-Breathers and the Fermi-Pasta-Ulam Problem
• Relaxation of classical many-body hamiltonians in one dimension
• Intermittent many-body dynamics at equilibrium
• The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems
• q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability
• Finite times to equipartition in the thermodynamic limit
• Double scaling in the relaxation time in the $\beta$-FPUT model
• The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior
• Equilibration of Quasi-Integrable Systems
• Weak and strong chaos in FPU models and beyond
• The Fermi-Pasta-Ulam problem and its underlying integrable dynamics: an approach through Lyapunov Exponents
• Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system

Cited by in corpus (12)

• Arbitrarily Weak Nonlinearity Can Destroy the Anderson Localization
• Wave Turbulence and thermalization in one-dimensional chains
• Nonintegrability and thermalization of one-dimensional diatomic lattices
• Thermalization of local observables in the $\alpha$-FPUT chain
• Thermalization of two- and three-dimensional classical lattices
• Finite temperature equilibrium density profiles of integrable systems in confining potentials
• Effect of pressure on thermalization of one-dimensional nonlinear chains
• The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices
• A general multi-wave quasi-resonance theory for lattice energy diffusion
• Universal route to thermalization in weakly-nonlinear one-dimensional chains
• Thermalization in asymmetric harmonic chains
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport