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关于液体、过冷液体和玻璃态系统能量景观的全球视角:势能景观系综。

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: the potential energy landscape ensemble.

作者信息

Wang Chengju, Stratt Richard M

机构信息

Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA.

出版信息

J Chem Phys. 2007 Dec 14;127(22):224503. doi: 10.1063/1.2801994.

Abstract

In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move--an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that deemphasizes the concept of potential barriers, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable. We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen [Phys. Rev. E 51, 4626 (1995)] of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its empirical mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.

摘要

原则上,多体系统的所有动力学复杂性都包含在原子运动的势能面上——这一观察结果表明,动力学的本质应该由这些势能面的几何形状决定。但是,控制长时间动力学的主要几何特征是什么呢?我们认为关键不在于势能面的局部极小值和鞍点,而在于表面的一种更全局的性质:其可达路径。为了使这个概念更精确,我们引入两个概念:(1)切换到一个新的系综,该系综淡化势能垒的概念;(2)在这个新系综中找到最优路径的方法。我们在本文中描述的势能面系综,将最大可达势能而非温度视为控制变量。我们在此表明,虽然这种方法在热力学上与正则系综等价,但它不仅避开了势垒的概念,还使我们能够定量描述势能面的连通性。我们通过对一种简单原子液体以及对玻璃形成液体的科布 - 安德森模型[《物理评论E》51, 4626 (1995)]进行计算来说明这些概念,在此过程中表明,科布 - 安德森模型的势能面在与其经验模式耦合转变相关的势能处似乎存在连通性转变。在我们的配套论文中,我们将探讨在势能面中寻找最有效路径的问题。

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