Silbermann Jörg R, Schoen Martin, Klapp Sabine H L
Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekretariat C7, Technische Universität Berlin, Strasse des 17, Juni 115, Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 1):011201. doi: 10.1103/PhysRevE.78.011201. Epub 2008 Jul 16.
We consider the dynamics of a single tagged particle in a two-dimensional system governed by Lennard-Jones interactions. Previous work based on the Mori-Zwanzig projection operator formalism has shown that the single-particles dynamics can be described via a generalized Langevin equation (GLE) which is exact within the harmonic approximation, that is, for a low-temperature solid [J. M. Deutch and R. Silbey, Phys. Rev. A 3, 2049 (1971)]. In the present work we explore to what an extent the GLE reproduces the effective dynamics under thermodynamic conditions where the harmonic approximation is no longer justified. To this end we compute characteristic time autocorrelation functions for the tagged particle in molecular dynamics simulations of the full system and compare these functions with those obtained from solving the GLE. At low temperatures we find excellent agreement between both data sets. Deviations emerge at higher temperatures which are, however, surprisingly small even in the high-temperature liquid phase.
我们考虑在由 Lennard-Jones 相互作用支配的二维系统中单个标记粒子的动力学。先前基于 Mori-Zwanzig 投影算符形式主义的工作表明，单粒子动力学可以通过广义 Langevin 方程（GLE）来描述，该方程在谐波近似下是精确的，即对于低温固体而言[J. M. Deutch 和 R. Silbey，《物理评论 A》3，2049（1971）]。在本工作中，我们探讨在谐波近似不再合理的热力学条件下，GLE 在多大程度上能再现有效动力学。为此，我们在全系统的分子动力学模拟中计算标记粒子的特征时间自相关函数，并将这些函数与通过求解 GLE 获得的函数进行比较。在低温下，我们发现两个数据集之间有极好的一致性。在较高温度下出现了偏差，然而，即使在高温液相中，这些偏差也小得出奇。
