Comment on 'Heavy (or large) ions in a fluid in an electric field: Thediffusion equation exactly following from the Fokker—Planck equation'[J. Chem. Phys. 129, 044903 (2008)]

摘要

In a recent article,1 Ferrari tackled the task of finding theexact diffusion equation (EDE) corresponding to the Klein-Kramers equation (KKE) with a spatially homogeneoustime-varying field. Apart from some straightforward exten-sions (see below), the diffusion equation (DE) found by Fer-rari was deduced more than 70 years ago by Ornstein andvan Wijk (hereafter O&vW), but their paper~2seems to haveslipped into oblivion. Second, Ferrari's treatment is validonly when all particles start with the same initial velocity;for distributed initial velocities, his conclusions conflict withseveral independent analyses. In recent years, othercontributors~(3,4)to this Journal have grappled with an issueclosely related to the problem discussed by Ferrari—namely,the replacement of the KKE with approximate descriptionsin position space; accordingly, I take this opportunity towiden the discussion by commenting on their articles aswell. For convenience, I will replace Ferrari's phrase "heavy(or large) ion" with the term "Brownian particle" and shortenthe latter to "B particle."