Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, China and School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
Phys Rev E. 2016 Jun;93(6):062112. doi: 10.1103/PhysRevE.93.062112. Epub 2016 Jun 7.
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
利用绝热连接，我们根据关联函数 h_{λ}(r,r^{'})，用虚构系统的关联函数 h_{λ}(r,r^{'})来表述自由能，其中相互作用 λu(r,r^{'})随着 λ从 0 逐渐变为 1。然后从非均匀奥恩斯坦-泽尔尼克方程中得到 h_{λ}(r,r^{'})，这两个方程构成了处理不均匀流体的一般液体状态框架。这两个方程还没有构成一个封闭的集合。在目前的工作中，我们使用封闭 c_{λ}(r,r^{'})≈-λβu(r,r^{'})，称为随机相位近似（RPA）。我们证明 RPA 与最初在理论框架内推导并用于带电粒子的变分高斯近似相同。我们将我们的广义 RPA 近似应用于高斯核模型和库仑电荷。
