Abstract
The results of variational solutions of the repeated ring and self-consistent repeated ring equations for the two-and three-dimensional overlapping Lorentz gas (LG), as formulated in a previous report, are presented. Calculations of the full velocity correlation function (VCF) for the 2D LG, including long-time tails, are compared with those from molecular dynamics. The trial functions chosen lead to predictions for the long-time tails that improve as the density of the scatterers is increased. At a value of 0.24 forρ* (=ρσ 2, whereρ is the density and σ the radius of scatterers), the self-consistent amplitudes of the long-time tail are within 40% of the molecular dynamics. A limited number of 3D results for the short-time behavior of the repeated ring VCF are presented. The 3D solutions agree with the molecular dynamics to within 10%.
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Cole, R.G., Keyes, T. The velocity correlation function for the Lorentz gas. J Stat Phys 51, 275–289 (1988). https://doi.org/10.1007/BF01015331
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DOI: https://doi.org/10.1007/BF01015331