Renormalized waves and discrete breathers in $\beta$-FPU chains

Abstract

We demonstrate via numerical simulation that in the \textit{strongly} nonlinear limit, the $\beta$-FPU system in thermal equilibrium behaves surprisingly like weakly nonlinear waves in properly renormalized normal variables. This arises because the collective effect of strongly nonlinear interactions effectively renormalizes linear dispersion frequency and leads to effectively weak interaction among these renormalized waves. Furthermore, we show that the dynamical scenario for thermalized $\beta$-FPU chains is spatially highly localized discrete breathers riding chaotically on spatially extended, renormalized waves.

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• Double scaling in the relaxation time in the $\beta$-FPUT model
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• Effect of discrete breathers on the specific heat of a nonlinear chain
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• Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean free paths
• Wave Turbulence and thermalization in one-dimensional chains
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• Universality of Energy Equipartition in One-dimensional Lattices
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Renormalized phonons in nonlinear lattices: A variational approach
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
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• Thermal conductance of the Fermi-Pasta-Ulam chains: Atomic to mesoscopic transition
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes
• Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
• The effect of dressing on thermalization of interacting waves
• Renormalized waves and thermalization of the Klein-Gordon equation: What sound does a nonlinear string make?
• Quasi-linear dynamics in nonlinear Schr\" odinger equation with periodic boundary conditions
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• Thermalization in asymmetric harmonic chains