Self-diffusion in fluids with weak long-range forces

Diffusion of a test particle in a homogeneous classical fluid with weak long-range forces is studied. The dominant mean-field effect (Vlasov's theory) vanishes for symmetry reasons. Dynamical phenomena follow then from fluctuations of the effective potential energy felt by the propagating particle. The kinetic equation corresponding to this mechanism is derived with the use of the multiple-time-scale method. Its structure resembles very much that of the (linearized) Balescu-Lenard equation of hot plasma theory. It is shown that the kinetic equation holds only if no phase transition occurs in the system. The thermalization of the diffusing particle and the high-temperature and Lorentz gas limits are discussed.