Relaxation in N-body simulations of spherical systems
  I present empirical measurements of the rate of relaxation in N-body
simulations of stable spherical systems and distinguish two separate types of
relaxation: energy diffusion that is largely independent of particle mass, and
energy exchange between particles of differing masses. While diffusion is
generally regarded as a Fokker-Planck process, it can equivalently be viewed as
the consequence of collective oscillations that are driven by shot noise.
Empirical diffusion rates scale as N^{-1} in inhomogeneous models, in agreement
with Fokker-Planck predictions, but collective effects cause relaxation to
scale more nearly as N^{-1/2} in the special case of a uniform sphere. I use
four different methods to compute the gravitational field, and a 100-fold range
in the numbers of particles in each case. I find the rate at which energy is
exchanged between particles of differing masses does not depend at all on the
force determination method, but I do find the energy diffusion rate is
marginally lower when a field method is used. The relaxation rate in 3D is
virtually independent of the method used because it is dominated by distant
encounters; any method to estimate the gravitational field that correctly
captures the contributions from distant particles must also capture their
statistical fluctuations and the collective modes they drive.
