Localization and Equipartition of Energy in the beta-FPU Chain : Chaotic Breathers

Abstract

The evolution towards equipartition in the $\beta$-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally unstable and to give rise to a striking localization process. The spontaneously created excitations have strong similarity with moving exact breathers solutions. But they have a finite lifetime and their dynamics is chaotic. These chaotic breathers are able to collect very efficiently the energy in the chain. Therefore their size grows in time and they can transport a very large quantity of energy. These features can be explained analyzing the dynamics of perturbed exact breathers of the FPU chain. In particular, a close connection between the Lyapunov spectrum of the chaotic breathers and the Floquet spectrum of the exact ones has been found. The emergence of chaotic breathers is convincingly explained by the absorption of high frequency phonons whereas a breather's metastability is for the first time identified. The lifetime of the chaotic breather is related to the time necessary for the system to reach equipartition. The equipartition time turns out to be dependent on the system energy density $\epsilon$ only. Moreover, such time diverges as ${\epsilon }^{-2}$ in the limit $\epsilon \to 0$ and vanishes as ${\epsilon }^{-1/4}$ for $\epsilon \to \infty$.

20 pages, Revtex - Submitted to Physica D

References in corpus (7)

• Discrete Breathers
• Mobility and Reactivity of Discrete Breathers
• The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems
• Movability of Localized Excitations in Nonlinear Discrete Systems - a Separatrix Problem
• Low energy chaos in the Fermi-Pasta-Ulam problem
• On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators
• The phase plane of moving discrete breathers

Cited by in corpus (54)

• The Fermi-Pasta-Ulam problem: 50 years of progress
• Simulating rare events in dynamical processes
• A route to thermalization in the $\alpha$-Fermi-Pasta-Ulam system
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Growth and decay of discrete nonlinear Schroedinger breathers interacting with internal modes or standing-wave phonons
• q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability
• On modulational instability and energy localization in anharmonic lattices at finite energy density
• Bushes of vibrational modes for Fermi-Pasta-Ulam chains
• Discrete breathers in Fermi-Pasta-Ulam lattices
• Renormalized waves and discrete breathers in $\beta$-FPU chains
• The Anti-FPU Problem
• Long-range energy transfer in proteins
• Fast Dynamics in a Model Metallic Glass-forming Material
• Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
• Energy Relaxation in Nonlinear One-Dimensional Lattices
• Large deviations of Lyapunov exponents
• Effect of discrete breathers on the specific heat of a nonlinear chain
• Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain
• Cooling nonlinear lattices toward localisation
• Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems
• Wavelet imaging of transient energy localization in nonlinear systems at thermal equilibrium: the case study of NaI crystals at high temperature
• Energy Localization in the Peyrard-Bishop DNA model
• Pattern formation and localization in the forced-damped FPU lattice
• Breathers and Thermal Relaxation in Fermi-Pasta-Ulam Arrays
• Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system
• Stretched--exponential relaxation in arrays of coupled rotators
• Weak chaos detection in the Fermi-Pasta-Ulam-$\alpha$ system using $q$-Gaussian statistics
• Interaction of a Kink-Soliton with a Breather in a Fermi-Pasta-Ulam Chain
• Self-organized escape of oscillator chains in nonlinear potentials
• Identifying rare chaotic and regular trajectories in dynamical systems with Lyapunov weighted path sampling
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
• Glassiness and Lack of Equipartition in Random Lasers: the common roots of Ergodicity Breaking in Disordered and Non-linear Systems
• Discrete Breathers in a Realistic Coarse-Grained Model of Proteins
• Energy Relaxation in Fermi-Pasta-Ulam Arrays
• Quantum breathers in a nonlinear Klein Gordon lattice
• Energy transfer in nonlinear network models of proteins
• Energy transport along FPU-beta chains containing binary isotopic disorder: Zero temperature systems
• Excitation of travelling multibreathers in anharmonic chains
• Existence of exponentially spatially localised breather solutions for lattices of nonlinearly coupled particles: Schauder's fixed point theorem approach
• Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure
• Extreme events due to localisation of energy
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations
• The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices
• A general multi-wave quasi-resonance theory for lattice energy diffusion
• Energy transfer mechanisms in a dipole chain: From energy equipartition to the formation of breathers
• Nonlinear response of a linear chain to weak driving
• Intensity pseudo-localized phase in the glassy random laser
• Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method
• Prethermalization in Fermi-Pasta-Ulam-Tsingou chains
• Periodic travelling wave solutions of discrete nonlinear Klein-Gordon lattices
• Quasi-stable Localized Excitations in the β-Fermi Pasta Ulam Tsingou System
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• The hidden role of coupled wave network topology on the dynamics of nonlinear lattices