DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
J Chem Phys. 2011 Sep 14;135(10):104102. doi: 10.1063/1.3623586.
In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, "NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface," J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1∕N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nosé-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.
在相关论文 [T. S. Ingebrigtsen、S. Toxvaerd、O. J. Heilmann、T. B. Schrøder 和 J. C. Dyre，“NVU 动力学。I. 恒势能超曲面上的测地线运动”，J. Chem. Phys.（即将出版）] 中，开发了一种在恒势能超曲面上追踪测地线的算法。在这里，将 NVU 动力学的模拟结果与其他四种动力学（确定性和随机动力学）的结果进行了比较。首先，通过模拟 Kob-Andersen 双 Lennard-Jones 液体、其 WCA 版本（即在对势能最小处进行截断）以及 Lennard-Jones 高斯液体，将 NVU 动力学与标准能量守恒牛顿 NVE 动力学进行了比较。我们发现所有探测到的量（径向分布函数、非相干中间散射函数和均方位移随时间的函数）的结果都相同。提出了 NVU 和 NVE 动力学在热力学极限下等效的论点；特别是，在 1∕N 的一阶近似下，这两种动力学给出了相同的时间自相关函数。在本文的最后部分，将 NVU 动力学与蒙特卡罗动力学、恒势能超曲面上小步随机游动的扩散动力学以及 Nosé-Hoover NVT 动力学进行了比较。如果将两种随机动力学的时间尺度缩放，以使单粒子扩散常数与 NVE 动力学的扩散常数相同，那么模拟结果表明，除了短时间之外，在低温下，所有五种动力学都是等效的。
