Chaos and the continuum limit in the gravitational N-body problem. II. Nonintegrable potentials.

This paper continues a numerical investigation of the statistical properties of "frozen-N orbits," i.e., orbits evolved in frozen, time-independent N-body realizations of smooth density distributions rho corresponding to both integrable and nonintegrable potentials, allowing for 10(2.5)10(3)-10(4), clear distinctions exist between the phase mixing of initially localized ensembles, which, in the continuum limit, exhibit regular versus chaotic behavior. Regular ensembles evolved in a frozen-N density distribution diverge as a power law in time, albeit more rapidly than ensembles evolved in the smooth distribution. Chaotic ensembles diverge in a fashion that is roughly exponential, albeit at a larger rate than that associated with the exponential divergence of the same ensemble evolved in smooth rho. For both regular and chaotic ensembles, finite-N effects are well mimicked, both qualitatively and quantitatively, by energy-conserving white noise with amplitude eta proportional, variant 1/N. This suggests strongly that earlier investigations of the effects of low amplitude noise on phase space transport in smooth potentials are directly relevant to real physical systems.