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.
Dolgopyat, D., Liverani, C. (2011). Energy transfer in a fast-slow Hamiltonian system. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 308(1), 201-225 [10.1007/s00220-011-1317-7].
Energy transfer in a fast-slow Hamiltonian system
LIVERANI, CARLANGELO
2011-11-01
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.File in questo prodotto:
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