Abstract

Systems with long-range forces behave very differently from those in which particles interact through short-range potentials. For systems with short-range forces, 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 interactions, equivalence between ensembles breaks down. In a microcanonical ensemble — in thermodynamic limit — such Hamiltonian systems do not evolve to the usual Maxwell-Boltzmann 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 obtain the final stationary state achieved by systems with long-range interactions. The theory is able to quantitatively predict both the density and the velocity distributions in the final stationary state, without any adjustable parameters [1,2,3].

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

[2] Y. Levin, R. Pakter, and F.B. Rizzato, Phys. Rev. E 78 , 021130 (2008); T. N. Teles, Y. Levin, and R. Pakter, Mon. Not. R. Astron. Soc. 417, L21 (2011).

[3] R. Pakter, and Y. Levin, Phys. Rev. Lett. 106, 200603 (2011).