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

Systems with unscreened long-range forces behave very differently from those in which particles interact through short-range potentials. For systems with short-range interactions, for arbitrary initial conditions, the final 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 final 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].

[1] Y. Levin, R. Pakter, F.B, Rizzato, T.N. Teles, and F.P.C. Benetti, Phys. Rep. 535, 1 (2014).

[2] Y. Levin, R. Pakter and T. N. Telles, Phys. Rev. Lett. 100, 040604 (2008).

[3] F. P. C. Benetti, A. C. Ribeiro-Teixeira, R. Pakter, and Y. Levin, Phys. Rev. Lett. 113, 100602 (2014).

[4] R. Pakter and Y. Levin, Phys. Rev. Lett. 121, 020602 (2018).