Slow energy dissipation in anharmonic oscillator chains

DOI10.1002/cpa.20280zbMath1169.82012arXiv0712.3884OpenAlexW2025369101WikidataQ56894406 ScholiaQ56894406MaRDI QIDQ5323023

Martin Hairer, Jonathan C. Mattingly

Publication date: 23 July 2009

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3884

zbMATH Keywords

Lyapunov functionFokker-Planck equationoscillatorsbreather

Mathematics Subject Classification ID

Related Items (26)

Nonequilibrium statistical mechanics of weakly stochastically perturbed system of oscillators ⋮ Non-equilibrium steady states for chains of four rotors ⋮ Asymptotic Localization of Energy in Nondisordered Oscillator Chains ⋮ Non-equilibrium steady states for networks of oscillators ⋮ Join-the-shortest queue diffusion limit in Halfin-Whitt regime: sensitivity on the heavy-traffic parameter ⋮ Damped and driven breathers and metastability ⋮ Recent progress on limit theorems for large stochastic particle systems ⋮ Energy dissipation in Hamiltonian chains of rotators ⋮ Numerical simulation of polynomial-speed convergence phenomenon ⋮ Quantitative rates of convergence to non-equilibrium steady state for a weakly anharmonic chain of oscillators ⋮ A note on Fisher information hypocoercive decay for the linear Boltzmann equation ⋮ Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations ⋮ Positive Harris recurrence for degenerate diffusions with internal variables and randomly perturbed time-periodic input ⋮ Join-the-shortest queue diffusion limit in Halfin-Whitt regime: tail asymptotics and scaling of extrema ⋮ Well-posedness and long time behavior of singular Langevin stochastic differential equations ⋮ Nonequilibrium statistical mechanics of a solid immersed in a continuum ⋮ Nonequilibrium steady states for certain Hamiltonian models ⋮ A noise-induced transition in the Lorenz system ⋮ Local asymptotic normality for shape and periodicity of a signal in the drift of a degenerate diffusion with internal variables ⋮ Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials ⋮ Existence of a nonequilibrium steady state for the nonlinear BGK equation on an interval ⋮ Geometric ergodicity of Langevin dynamics with Coulomb interactions ⋮ The optimal spectral gap for regular and disordered harmonic networks of oscillators ⋮ How hot can a heat bath get? ⋮ Weighted L ²-contractivity of Langevin dynamics with singular potentials ⋮ Sensitivity of steady states in a degenerately damped stochastic Lorenz system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Subgeometric rates of convergence of \(f\)-ergodic strong Markov processes
• On polynomial mixing bounds for stochastic differential equations
• Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures
• Entropy production in nonlinear, thermally driven Hamiltonian systems
• Exponential convergence to non-equilibrium stationary states in classical statistical mechanics
• Spectral properties of hypoelliptic operators
• Non-equilibrium statistical mechanics of strongly anharmonic chains of oscillators.
• Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
• Perturbation theory for linear operators.
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Towards a derivation of Fourier's law for coupled anharmonic oscillators
• On the essential spectrum
• On the essential spectrum of partial differential boundary problems
• Stability and Control of Stochastic Systems with Wide-band Noise Disturbances. I
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• Geometric Numerical Integration

This page was built for publication: Slow energy dissipation in anharmonic oscillator chains