Dressed diffusion and friction coefficients in inhomogeneous
  multicomponent self-gravitating systems
  General self-consistent expressions for the coefficients of diffusion and
dynamical friction in a stable, bound, multicomponent self-gravitating and
inhomogeneous system are derived. They account for the detailed dynamics of the
colliding particles and their self-consistent dressing by collective
gravitational interactions. The associated Fokker-Planck equation is shown to
be fully consistent with the corresponding inhomogeneous Balescu-Lenard
equation and, in the weak self-gravitating limit, to the inhomogeneous Landau
equation. Hence it provides an alternative derivation to both and demonstrates
their equivalence. The corresponding stochastic Langevin equations are
presented: they can be a practical alternative to numerically solving the
inhomogeneous Fokker-Planck and Balescu-Lenard equations. The present formalism
allows for a self-consistent description of the secular evolution of different
populations covering a spectrum of masses, with a proper accounting of the
induced secular mass segregation, which should be of interest to various
astrophysical contexts, from galactic centers to protostellar discs.
