论文标题
精确确定来自多体系统的成对统计数据的对相互作用，
Precise Determination of Pair Interactions from Pair Statistics of Many-Body Systems In and Out of Equilibrium
论文作者
论文摘要
The determination of the pair potential $v({\bf r})$ that accurately yields an equilibrium state at positive temperature $T$ with a prescribed pair correlation function $g_2({\bf r})$ or corresponding structure factor $S({\bf k})$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding inverse统计力学问题具有深远的影响。最近，张和Torquato猜想，任何可实现的$ g_2（{\ bf r}）$或$ s（{\ bf k}）$对应于与翻译不变的非平衡系统相对应的。测试该猜想的非平衡系统以及非平凡平衡状态需要改善反相反的方法。我们已经设计了一种新型的优化算法，以找到与正常温度下的一般翻译失调多体平衡或非平衡系统相对应的有效对电势。该方法利用了潜在功能的参数式基础函数家族，其初始形式由统计机械理论决定的小和大距离行为告知。随后，一种非线性优化技术被用来最大程度地减少目标函数，该目标函数都包含了目标对相关函数$ g_2（{\ bf r}）$和结构因子$ s（{\ bf k}）$，从而非常准确地捕获了小和大距离的相关性。为了说明我们方法的多功能性和功能，我们准确地确定了以下四个不同目标系统的有效对相互作用。我们发现，优化的对电势生成相应的对统计信息，这些统计数据将其相应目标与总$ L_2 $ -Norm误差相匹配，该误差的数量级比以前的方法小。
The determination of the pair potential $v({\bf r})$ that accurately yields an equilibrium state at positive temperature $T$ with a prescribed pair correlation function $g_2({\bf r})$ or corresponding structure factor $S({\bf k})$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato conjectured that any realizable $g_2({\bf r})$ or $S({\bf k})$ corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised a novel optimization algorithm to find effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function $g_2({\bf r})$ and structure factor $S({\bf k})$ so that the small- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total $L_2$-norm errors that are an order of magnitude smaller than that of previous methods.
