Collisionless Relaxation of Stellar Systems

The objective of the work summarised here has been to exploit and extend ideas from plasma physics and accelerator dynamics to formulate a unified description of collisionless relaxation that views violent relaxation, Landau damping, and phase mixing as (manifestations of) a single phenomenon. This approach embraces the fact that the collisionless Boltzmann equation (CBE), the basic object of the theory, is an infinite-dimensional Hamiltonian system, with the distribution function f playing the role of the fundamental dynamical variable, and that, interpreted appropriately, an evolution described by the {\it CBE} is no different fundamentally from an evolution described by any other Hamiltonian system. Equilibrium solutions correspond to extremal points of the Hamiltonian subject to the constraints associated with Liouville's Theorem. Stable equilibria correspond to energy minima. The evolution of a system out of equilibrium involves (in general nonlinear) phase space oscillations which may -- or may not -- interfere destructively so as to damp away.