Diffusion dynamics of classical systems driven by an oscillatory force

François Castella (1) , Pierre Degond (2) , Thierry Goudon (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 SIMPAF - SImulations and Modeling for PArticles and Fluids

We investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to the sum of a fixed, confining, Hamiltonian, and a small time-oscillating perturbation. Additionally, the equation involves an interaction operator which projects the distribution function onto functions of the fixed Hamiltonian. The paper aims at providing a classical counterpart to the derivation of rate equations from the atomic Bloch equations. Here, the homogenization procedure leads to a diffusion equation in the energy variable. The presence of the interaction operator regularizes the limit process and leads to finite diffusion coefficients.

Domaines: Analyse numérique [math.NA]

François Castella, Pierre Degond, Thierry Goudon. Diffusion dynamics of classical systems driven by an oscillatory force. Journal of Statistical Physics, 2006, 124 (2-4), pp.913-950. ⟨10.1007/s10955-006-9071-5⟩. ⟨hal-00449422⟩