Comparison of minimum-action and steepest-descent paths in gradient systems.
Comparison of minimum-action and steepest-descent paths in gradient systems.
复制标题
梯度系统中最小作用路径和最速下降路径的比较
DOI：
10.1103/physreve.93.022307
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Rogal
中科院分区：
文献类型：
--
作者：
G. Diaz Leines;J. Rogal
在高维复杂的势能面上，识别局部极小值之间的最可能的过渡机制是一项具有挑战性的任务。通常最速下降路径与最小能量路径互换使用，并与最可能的路径相关联。在这里，我们将复杂能量景观中最速下降路径的含义与布朗动力学作用泛函最小化的轨迹的路径积分公式进行比较。特别是，对于具有分叉点和多个最小值和鞍点的能量景观，可以存在与连接两个预定状态但与最大似然路径大不相同的特定鞍相关联的若干最陡下降路径。然而，最小动作路径另外考虑了沿轨迹的标量功沿着。最小化标量工作可以在不同梯度系统中识别最可能的路径时不那么模糊。它也可以用来区分连接反应物和产物状态的多个最速下降路径。我们说明，在复杂的能源景观系统的最陡下降路径的仔细评估是明智的。在这里，对动作的评估可以提供关于最可能路径的分析和描述的有价值的信息。
On high-dimensional and complex potential energy surfaces, the identification of the most likely mechanism for the transition between local minima is a challenging task. Usually the steepest-descent path is used interchangeably with the minimum-energy path and is associated with the most likely path. Here we compare the meaning of the steepest-descent path in complex energy landscapes to the path integral formulation of a trajectory that minimizes the action functional for Brownian dynamics. In particular, for energy landscapes with bifurcation points and multiple minima and saddle points, there can be several steepest-descent paths associated with specific saddles that connect two predetermined states but largely differ from the path of maximum likelihood. The minimum-action path, however, additionally takes into account the scalar work along the trajectory. Minimizing the scalar work can be less ambiguous in the identification of the most likely path in different gradient systems. It can also be used to distinguish between multiple steepest-descent paths that connect reactant and product states. We illustrate that in systems with complex energy landscapes a careful assessment of the steepest-descent path is thus advisable. Here the evaluation of the action can provide valuable information on the analysis and description of the most likely path.