Vlasov limit for a chain of oscillators with Kac potentials

Abstract

We consider a chain of anharmonic oscillators with local mean field interaction and long-range stochastic exchanges of velocity. Even if the particles are not exchangeable, we prove the convergence of the empirical measure associated with this chain to a solution of a Vlasov-type equation. We then use this convergence to prove energy diffusion for a restricted class of anharmonic potentials.

References in corpus (6)

• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
• Thermal Conductivity for a Momentum Conserving Model
• Superdiffusion of energy in a chain of harmonic oscillators with noise
• Energy current correlation in solvable long-range interacting systems
• A family of fractional diffusion equations derived from stochastic harmonic chains with long-range interactions