Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions

摘要

Systems with long-range (LR) forces, for which the interaction potentialdecays with the interparticle distance with an exponent smaller than thedimensionality of the embedding space, remain an outstanding challenge tostatistical physics. The internal energy of such systems lacks extensivity andadditivity. Although the extensivity can be restored by scaling the interactionpotential with the number of particles, the non-additivity still remains. Lackof additivity leads to inequivalence of statistical ensembles. Before relaxingto thermodynamic equilibrium, isolated systems with LR forces become trapped inout-of-equilibrium quasi-stationary state (qSS), the lifetime of which divergeswith the number of particles. Therefore, in thermodynamic limit LR systems willnot relax to equilibrium. The qSSs are attained through the process ofcollisionless relaxation. Density oscillations lead to particle-waveinteractions and excitation of parametric resonances. The resonant particlesescape from the main cluster to form a tenuous halo. Simultaneously, this coolsdown the core of the distribution and dampens out the oscillations. When allthe oscillations die out the ergodicity is broken and a qSS is born. In thisreport, we will review a theory which allows us to quantitatively predict theparticle distribution in the qSS. The theory is applied to various LRinteracting systems, ranging from plasmas to self-gravitating clusters andkinetic spin models.