Kinetic theory of onedimensional homogeneous longrange interacting systems sourced by 1 /N^{2} effects
Abstract
The longterm dynamics of longrange interacting N body systems can generically be described by the BalescuLenard kinetic equation. However, for onedimensional homogeneous systems, this collision operator exactly vanishes by symmetry. These systems undergo a kinetic blocking, and cannot relax as a whole under 1 /N resonant effects. As a result, these systems can only relax under 1 /N^{2} effects, and their relaxation is drastically slowed down. In the context of the homogeneous Hamiltonian mean field model, we present a closed and explicit kinetic equation describing selfconsistently the very longterm evolution of such systems, in the limit where collective effects can be neglected, i.e., for dynamically hot initial conditions. We show in particular how that kinetic equation satisfies an H theorem that guarantees the unavoidable relaxation to the Boltzmann equilibrium distribution. Finally, we illustrate how that kinetic equation quantitatively matches with the measurements from direct N body simulations.
 Publication:

Physical Review E
 Pub Date:
 November 2019
 DOI:
 10.1103/PhysRevE.100.052142
 arXiv:
 arXiv:1907.07213
 Bibcode:
 2019PhRvE.100e2142F
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 15 pages, 4 figures, submitted to PRE