Energy transfer in a fast-slow Hamiltonian system

Abstract

We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a non linear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems.

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• Nonequilibrium statistical mechanics of weakly stochastically perturbed system of oscillators
• On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas
• Role of conserved quantities in Fourier's law for diffusive mechanical systems
• Local thermal equilibrium for certain stochastic models of heat transport
• Energy transport through rare collisions
• Equidistribution for standard pairs in planar dispersing billiard flows
• Nonconventional limit theorems in averaging