微观描述下的非局部静电场理论
Nonlocal Electrostatic Field Theory from Microscopic Description
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中文总结 AI 辅助
该研究从微观运动方程构建统一平均场福克 - 普朗克方程，用于描述非局部非线性系统非平衡静电学，得出广义泊松 - 玻尔兹曼方程和静电自由能表达式，在线性近似下获各向异性磁化率，实现静电局部线性响应反转。
中文摘要 AI 辅助
软材料中电场的研究要么汇聚于非线性理论中对类点粒子（局部）的研究，要么汇聚于非局部线性理论中对有限尺寸粒子的使用。本文从微观运动方程出发，构建了一个统一的平均场福克 - 普朗克方程，描述非局部非线性系统的非平衡静电学。得到了此类系统的广义泊松 - 玻尔兹曼方程及其静电自由能表达式。在线性近似下，在各向同性流体中得到了各向异性磁化率，实现了静电学中的局部线性响应反转。
英文摘要
The study of electric fields in soft materials converges either to the study of point-like particles (local) in nonlinear theories or to the use of particles with finite sizes in nonlocal linear theories. In this work we start from the microscopic equations of motion and construct a unified mean field Fokker-Planck equation that describes the non-equilibrium electrostatics of nonlocal nonlinear systems. We obtain a generalized Poisson-Boltzmann equation for such systems as well as their electrostatic free energy expression. In the linear approximation we obtain an anisotropic susceptibility in an isotropic fluid which allows for local linear response inversion in electrostatics.
