q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability

Abstract

The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here q-Breathers (QB). They are characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.

29 pages

References in corpus (7)

• The Fermi-Pasta-Ulam problem: 50 years of progress
• q-Breathers and the Fermi-Pasta-Ulam Problem
• Discrete breathers in Fermi-Pasta-Ulam lattices
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
• Localization and Coherence in Nonintegrable Systems
• Energy Relaxation in Nonlinear One-Dimensional Lattices
• Discrete breathers in thermal equilibrium: distributions and energy gaps

Cited by in corpus (44)

• Phononic Frequency Combs via Nonlinear Resonances
• Intermittent many-body dynamics at equilibrium
• Energy localization on q-tori, long term stability and the interpretation of FPU recurrences
• The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior
• Conserved quantities and dual turbulent cascades in Anti-de Sitter spacetime
• Islands of stability and recurrence times in AdS
• The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and resonance overlap criteria
• Effect of discrete breathers on the specific heat of a nonlinear chain
• Dynamical glass in weakly non-integrable Klein-Gordon chains
• Tail resonances of FPU q-breathers and their impact on the pathway to equipartition
• Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices
• Application of the GALI Method to Localization Dynamics in Nonlinear Systems
• q-breathers in finite two- and three-dimensional nonlinear acoustic lattices
• Scaling properties of $q$-breathers in nonlinear acoustic lattices
• Weak chaos detection in the Fermi-Pasta-Ulam-$\alpha$ system using $q$-Gaussian statistics
• Quantum q-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons
• Universal law of thermalization for one-dimensional perturbed Toda lattices
• Instabilities and relaxation to equilibrium in long-range oscillator chains
• Self-organized escape of oscillator chains in nonlinear potentials
• Behavior and Breakdown of Higher-Order Fermi-Pasta-Ulam-Tsingou Recurrences
• Discrete Symmetry and Stability in Hamiltonian Dynamics
• Low-dimensional q-Tori in FPU Lattices: Dynamics and Localization Properties
• Stringlet Excitation Model of the Boson Peak
• Boundary effects on quantum q-breathers in a Bose-Hubbard chain
• Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem
• $q$-Breathers in finite lattices: nonlinearity and weak disorder
• q-breathers in Discrete Nonlinear Schroedinger lattices
• Thermalization of local observables in the $\alpha$-FPUT chain
• Stability of non-time-reversible phonobreathers
• The $\beta$ Fermi-Pasta-Ulam-Tsingou Recurrence Problem
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Stable and unstable periodic orbits in the one dimensional lattice ${\varphi }^4$ theory
• Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes
• Freezing of the optical--branch energy in a diatomic FPU chain
• Analysis of ballistic transport and resonance in the $\alpha$-Fermi-Pasta-Ulam-Tsingou model
• The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices
• Energy-recurrence Breakdown and Chaos in Disordered Fermi-Pasta-Ulam-Tsingou Lattices
• Prethermalization in Fermi-Pasta-Ulam-Tsingou chains
• q-Breathers in Discrete Nonlinear Schroedinger arrays with weak disorder
• Adiabatic Gauge Potential as a Tool for Detecting Chaos in Classical Systems
• Extensive packet excitations in FPU and Toda lattices
• Kolmogorov algorithm for isochronous Hamiltonian systems
• Stages of dynamics in the Fermi-Pasta-Ulam system as probed by the first Toda integral
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization