Relaxation of a test particle in systems with long-range interactions: diffusion coefficient and dynamical friction |
| |
Authors: | P H Chavanis |
| |
Institution: | (1) Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France |
| |
Abstract: | We study the relaxation of a test particle immersed
in a bath of field particles interacting via weak long-range
forces. To order 1/N in the N→+∞ limit, the
velocity distribution of the test particle satisfies a
Fokker-Planck equation whose form is related to the Landau and
Lenard-Balescu equations in plasma physics. We provide explicit
expressions for the diffusion coefficient and friction force in the
case where the velocity distribution of the field particles is
isotropic. We consider (i) various dimensions of space d=3,2 and
1; (ii) a discret spectrum of masses among the particles; (iii)
different distributions of the bath including the Maxwell
distribution of statistical equilibrium (thermal bath) and the step
function (water bag). Specific applications are given for
self-gravitating systems in three dimensions, Coulombian systems in
two dimensions and for the HMF model in one dimension. |
| |
Keywords: | 05 20 -y Classical statistical mechanics 05 45 -a Nonlinear dynamics and chaos |
本文献已被 SpringerLink 等数据库收录! |
|