用最小生成树计算能量景观网络的渐近谱
Computing the Asymptotic Spectrum for Networks Representing Energy Landscapes using the Minimal Spanning Tree
摘要：
近年来，亚稳性的概念引起了人们的极大兴趣。随机网络的生成矩阵的谱分解揭示了系统中所有的转移过程。假设存在一个由谱隙分离的低本征值组，导致动力学的因式分解，已成为一个流行的主题。我们考虑随机网络表示势能景观的状态和边缘分别对应于局部极小值和过渡状态，和成对的转移率由Arkuis公式。利用最小生成树，我们从最低群出发，构造了生成矩阵的特征值和特征向量的渐近性。这种结构产生了一个有效的算法计算的渐近谱适合于大型和复杂的网络。我们将其应用到威尔士的Lennard-Jones-38网络，该网络具有71887个状态和119853个边缘，其中潜在的势能景观具有双漏斗结构。我们的研究结果表明，亚稳性的概念，应适用于照顾这个系统。特别是，对于完整的网络，没有显着的光谱间隙分离的特征值对应的出口从更宽和更浅的二十面体漏斗在任何合理的温度范围。
英文摘要：
The concept of metastability has caused a lot of interest in recent years. The spectral decomposition of the generator matrix of a stochastic network exposes all of the transition processes in the system. The assumption of the existence of a low lying group of eigenvalues separated by a spectral gap, leading to factorization of the dynamics, has become a popular theme. We consider stochastic networks representing potential energy landscapes where the states and the edges correspond to local minima and transition states respectively, and the pairwise transition rates are given by the Arrhenuis formula. Using the minimal spanning tree, we construct the asymptotics for eigenvalues and eigenvectors of the generator matrix starting from the low lying group. This construction gives rise to an efficient algorithm for computing the asymptotic spectrum suitable for large and complex networks. We apply it to Wales's Lennard-Jones-38 network with 71887 states and 119853 edges where the underlying potential energy landscape has a double-funnel structure. Our results demonstrate that the concept of metastability should be applied with care to this system. In particular, for the full network, there is no significant spectral gap separating the eigenvalue corresponding to the exit from the wider and shallower icosahedral funnel at any reasonable temperature range.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
