Kinetic Properties of a One-Dimensional Coulomb Gas

摘要

The BBKGY equations for N identical, impenetrable, charged particles which move in one dimension and lie in a charge neutralizing background, are shown to separate into N uncoupled equations for the sequence of N reduced distributions. The potential relevant to any subgroup of s adjoining particles is that of an s-dimensional harmonic oscillator whose frequency is the plasma frequency of the aggregate. The s-particle spatial equilibrium distribution reveals that particle vibrations remain centered about fixed, uniformly distributed sites as rho/T goes from zero to infinity, where rho is particle density and T is temperature. Thus it is concluded that the system suffers no change in phase for all rho and T. (Author)