Kinetic theory with angle-action variables

Details Kinetic theory with angle-action variables Kinetic theory with angle-action variables

2006-04-18

arxiv.org/abs/cond-mat/0604414v2

Physica A, 377, 469 (2007)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the distribution function of the system as a whole due to resonances between different orbits. This equation is written in angle-action variables. It conserves mass and energy and increases the Boltzmann entropy (H-theorem). Using a thermal bath approximation, we derive a Fokker-Planck equation that describes the relaxation of a test particle towards the Boltzmann distribution under the combined effect of diffusion and friction terms. We mention some analogies with the kinetic theory of point vortices in two-dimensional hydrodynamics. We also stress the limitations of our approach and the connection with recent works.

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