Time scale separation leads to position-dependent diffusion along a slow coordinate
Time scale separation leads to position-dependent diffusion along a slow coordinate
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DOI：
10.1063/1.3626215
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发表时间：
2011-08-21
影响因子：
4.4
通讯作者：
Szabo, Attila
中科院分区：
文献类型：
--
作者：
Berezhkovskii, Alexander;Szabo, Attila
当时间尺度分离时，可以通过快变量的绝热消除来获得慢变量动力学的有效描述。例如，对于二维各向异性朗之万动力学，传统程序会得出涉及平均力势的慢坐标朗之万方程。沿该坐标的摩擦常数保持不变。在这里，我们表明，通过使用与位置相关的摩擦力，可以通过使用类柯克伍德公式与实际力和平均力之差的自相关函数的时间积分相关，来获得对慢速动力学的更准确但仍然是马尔可夫的描述。结果被推广到许多维度，其中慢速或反应坐标是笛卡尔坐标的任意函数。当快变量实际上是一维时，沿慢坐标的附加摩擦可以以任意势的封闭形式表示。对于具有蜿蜒中心线的不同横截面的圆柱形对称通道，我们的解析表达式立即产生位置相关扩散系数的 Zwanzig-Bradley 公式的多维版本。 [doi:10.1063/1.3626215]
When there is a separation of time scales, an effective description of the dynamics of the slow variables can be obtained by adiabatic elimination of fast ones. For example, for anisotropic Langevin dynamics in two dimensions, the conventional procedure leads to a Langevin equation for the slow coordinate that involves the potential of the mean force. The friction constant along this coordinate remains unchanged. Here, we show that a more accurate, but still Markovian, description of the slow dynamics can be obtained by using position-dependent friction that is related to the time integral of the autocorrelation function of the difference between the actual force and the mean force by a Kirkwood-like formula. The result is generalized to many dimensions, where the slow or reaction coordinate is an arbitrary function of the Cartesian coordinates. When the fast variables are effectively one-dimensional, the additional friction along the slow coordinate can be expressed in closed form for an arbitrary potential. For a cylindrically symmetric channel of varying cross section with winding centerline, our analytical expression immediately yields the multidimensional version of the Zwanzig-Bradley formula for the position-dependent diffusion coefficient. [doi:10.1063/1.3626215]