Kalinay Pavol
Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovak Republic.
J Chem Phys. 2007 May 21;126(19):194708. doi: 10.1063/1.2734148.
A particle diffusing in a two-dimensional (2D) container, shaped as a simplified configuration space of two passing 2D circular particles in a flat channel, is considered. The mean first passage time through one absorbing boundary is calculated using the one-dimensional Fick-Jacobs equation and its modification; both derived by mapping the 2D diffusion equation onto the longitudinal ("reaction") coordinate. The obtained results are compared with the hopping time, defined as the inverted lowest eigenvalue of the full 2D problem. The comparison shows that the mapped equations give reliable results, in contrast to predictions of the simplest concept of the transition state theory.
考虑一个在二维（2D）容器中扩散的粒子，该容器形状为扁平通道中两个通过的二维圆形粒子的简化构型空间。通过将二维扩散方程映射到纵向（“反应”）坐标上推导得到的一维菲克 - 雅各布斯方程及其修正形式，计算了穿过一个吸收边界的平均首次通过时间。将所得结果与跳跃时间进行比较，跳跃时间定义为完整二维问题的最低特征值的倒数。比较结果表明，与过渡态理论最简单概念的预测相反，映射方程给出了可靠的结果。
