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Perturbation theory for the effective diffusion constant in a medium of random scatterer

机译:介质中有效扩散常数的微扰理论   随机散射体

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摘要

We develop perturbation theory and physically motivated resummations of theperturbation theory for the problem of a tracer particle diffusing in a randommedia. The random media contains point scatterers of density $\rho$ uniformlydistributed through out the material. The tracer is a Langevin particlesubjected to the quenched random force generated by the scatterers. Via ourperturbative analysis we determine when the random potential can beapproximated by a Gaussian random potential. We also develop a self-similarrenormalisation group approach based on thinning out the scatterers, thisscheme is similar to that used with success for diffusion in Gaussian randompotentials and agrees with known exact results. To assess the accuracy of thisapproximation scheme its predictions are confronted with results obtained bynumerical simulation.
机译:针对示踪剂粒子在随机介质中扩散的问题,我们开发了微扰理论和该微扰理论的物理激励再现。随机介质包含在整个材料中均匀分布的密度为\\ rho $的点散射体。示踪剂是朗格文粒子,它们受到散射器产生的猝灭随机力的作用。通过微扰分析,我们确定何时可以用高斯随机势近似随机势。我们还在稀疏散射体的基础上开发了一种自相似的归一化分组方法,该方案类似于成功用于高斯随机势扩散的方案,并且与已知的精确结果一致。为了评估该近似方案的准确性,其预测面临着通过数值模拟获得的结果。

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