Asymptotic analysis of the Green–Kubo formula
Asymptotic analysis of the Green–Kubo formula
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Green-Kubo 公式的渐近分析
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发表时间：
2010
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通讯作者：
G. Pavliotis
中科院分区：
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作者：
G. Pavliotis
本文详细研究了自扩散系数Green-Kubo公式的各种不同界限。首先，另一种表示形式的格林-久保公式的泊松方程的解决方案时，微观动力学是马尔可夫推导。然后在Golden & Papanicolaou（1983，Bounds for effective parameters of heterogeneous media by analytic continuation. Commun.数学物理，90，473-491）和Avellaneda & Majda（1991，An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flow. Commun.数学物理，138，339-391）用于获得扩散张量的对称和反对称部分的Stieltjes积分表示公式。不可逆的微观动力学的扩散系数的影响进行了分析和各种物理利益的渐近极限进行了研究。几个例子证实了我们的理论的研究结果。
A detailed study of various distinguished limits of the Green-Kubo formula for the self-diffusion coefficient is presented in this paper. First, an alternative representation of the Green-Kubo formula in terms of the solution of a Poisson equation is derived when the microscopic dynamics is Markovian. Then the techniques developed in Golden & Papanicolaou (1983, Bounds for effective parameters of heterogeneous media by analytic continuation. Commun. Math. Phys., 90, 473-491) and Avellaneda & Majda (1991, An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows. Commun. Math. Phys., 138, 339-391) are used to obtain a Stieltjes integral representation formula for the symmetric and antisymmetric parts of the diffusion tensor. The effect of irreversible microscopic dynamics on the diffusion coefficient is analysed and various asymptotic limits of physical interest are studied. Several examples are presented that confirm the findings of our theory.