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Diffusion Dynamics of Classical Systems Driven by an Oscillatory Force

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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.

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Authors and Affiliations

  1. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France

    F. Castella

  2. MIP, UMR 5640 (CNRS-UPS-INSA), Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex, France

    P. Degond

  3. Team SIMPAF–INRIA Futurs & Labo. Paul Painlevé, UMR 8524, Université des Sciences et Technologies Lille 1, F-59655, Villeneuve d'Ascq Cedex, France

    Th. Goudon

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  1. F. Castella
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  2. P. Degond
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  3. Th. Goudon
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Correspondence to F. Castella.

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AMS Subject classification: 74Q10, 35Q99, 35B25, 82C70

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Castella, F., Degond, P. & Goudon, T. Diffusion Dynamics of Classical Systems Driven by an Oscillatory Force. J Stat Phys 124, 913–950 (2006). https://doi.org/10.1007/s10955-006-9071-5

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  • DOI: https://doi.org/10.1007/s10955-006-9071-5

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