Diffusion and localization in the two-dimensional Lorentz model

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Abstract
The validity of a recently proposed theory of the two-dimensional Lorentz model with overlap is examined by direct comparison of theoretical results with molecular-dynamics data in both the diffusion and localization phases. The diffusion coefficient, the shortand intermediate-time behavior of the velocity correlations, and the long-time velocity-correlation decay exhibit reasonable agreement between theory and simulation if considered as functions of the scatterer density measured relative to the percolation density. In particular, the observed but previously unexplained density variation of the effective long-time exponent of the velocity-autocorrelation function is obtained.