Condensed Matter Seminar: Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions

Systems with unscreened long-range forces behave very di erently from those in which particles interact through short-range potentials. For systems with short-range interactions, for arbitrary initial conditions, the nal stationary state corresponds to the thermodynamic equilibrium and can be described equivalently by either a microcanonical, canonical, or a grand-canonical ensemble. On the other hand, for systems with unscreened long-range forces, equivalence between ensembles breaks down. Isolated long-range interacting systems | in the thermodynamic limit | do not evolve to the usual Boltzmann-Gibbs equilibrium, but become trapped in a non-ergodic stationary state which explicitly depends on the initial particle distribution. In this talk, a theoretical framework will be presented which allows us to predict the nal stationary state to which a long-range interactioning system will evolve. The theory is able to quantitatively account for both density and velocity distributions in the stationary state, without any adjustable parameters [1]. Examples of the application of the theory will be drawn from plasma physics [2], self-gravitating systems [3], and 2d fluid dynamics [4].