Diffusion Dynamics of Classical Systems Driven by an Oscillatory Force |
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| Authors: | F Castella P Degond Th Goudon |
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| Institution: | (1) IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France;(2) MIP, UMR 5640 (CNRS-UPS-INSA), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France;(3) Team SIMPAF–INRIA Futurs & Labo. Paul Painlevé, UMR 8524, Université des Sciences et Technologies Lille 1, F-59655 Villeneuve d'Ascq Cedex, France |
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| Abstract: | 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.
AMS Subject classification: 74Q10, 35Q99, 35B25, 82C70 |
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| Keywords: | Kinetic equation homogenization diffusion limit |
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