Kinetic theory of onedimensional homogeneous longrange interacting systems with an arbitrary potential of interaction
Abstract
FiniteN effects unavoidably drive the longterm evolution of longrange interacting N body systems. The BalescuLenard kinetic equation generically describes this process sourced by 1 /N effects but this kinetic operator exactly vanishes by symmetry for onedimensional homogeneous systems: such systems undergo a kinetic blocking and cannot relax as a whole at this order in 1 /N . It is therefore only through the much weaker 1 /N^{2} effects, sourced by threebody correlations, that these systems can relax, leading to a much slower evolution. In the limit where collective effects can be neglected, but for an arbitrary pairwise interaction potential, we derive a closed and explicit kinetic equation describing this very longterm evolution. We show how this kinetic equation satisfies an H theorem while conserving particle number and energy, ensuring the unavoidable relaxation of the system toward the Boltzmann equilibrium distribution. Provided that the interaction is longrange, we also show how this equation cannot suffer from further kinetic blocking, i.e., the 1 /N^{2} dynamics is always effective. Finally, we illustrate how this equation quantitatively matches measurements from direct N body simulations.
 Publication:

Physical Review E
 Pub Date:
 November 2020
 DOI:
 10.1103/PhysRevE.102.052110
 arXiv:
 arXiv:2007.14685
 Bibcode:
 2020PhRvE.102e2110F
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 15 pages, 3 figures, submitted to Phys. Rev. E