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摘要翻译：
我们给出了相互作用布朗粒子平衡系统中密度涨落随时间变化的理论的图解形式。为了便于导出图解展开式，我们引入了一个由正交化多粒子密度涨落组成的基。我们得到了正交化密度涨落与时间相关的精确运动方程族。为了简化这个层次结构，我们忽略了高阶簇展开项对顶点的贡献。所得方程组的迭代解可以用三腿顶点和四腿顶点的图表示。我们分析了随时间变化的密度相关函数的图解级数的结构，得到了可约和不可约记忆函数的图解解释。后一个函数的单环自洽近似与以前用投影算子方法导出的布朗系统的模耦合近似是一致的。
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英文标题：
《Dynamics of interacting Brownian particles: a diagrammatic formulation》
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作者：
Grzegorz Szamel
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.
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PDF链接：
https://arxiv.org/pdf/705.3645
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