Abstract.

We determine the non-local stress autocorrelation tensor in an homogeneous and isotropic system of interacting Brownian particles starting from the Smoluchowski equation of the configurational probability density. In order to relate stresses to particle displacements as appropriate in viscoelastic states, we go beyond the usual hydrodynamic description obtained in the Zwanzig-Mori projection-operator formalism by introducing the proper irreducible dynamics following Cichocki and Hess, and Kawasaki. Differently from these authors, we include transverse contributions as well. This recovers the expression for the stress autocorrelation including the elastic terms in solid states as found for Newtonian and Langevin systems, in case that those are evaluated in the overdamped limit. Finally, we argue that the found memory function reduces to the shear and bulk viscosity in the hydrodynamic limit of smooth and slow fluctuations and derive the corresponding hydrodynamic equations.

Graphical abstract

中文翻译：

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布朗粒子的应力相关函数和线性响应

摘要。

我们从构型概率密度的Smoluchowski方程出发，确定相互作用布朗粒子的均质各向同性系统中的非局部应力自相关张量。为了将应力与粘弹性状态下的粒子位移适当地联系起来，我们超越了在Zwanzig-Mori投影算子形式主义中获得的通常的流体力学描述，通过在Cichocki和Hess以及Kawasaki之后引入适当的不可约动力学来进行描述。与这些作者不同的是，我们也包括横向贡献。这可以恢复应力自相关的表达式，其中包括在牛顿系统和Langevin系统中发现的固态弹性项（如果以超阻尼极限进行评估）。最后，

图形概要