Laboratoire Navier, UMR 8205, École des Ponts, IFSTTAR, CNRS, UPE, Champs-sur-Marne, France.
Phys Rev E. 2017 Nov;96(5-1):052101. doi: 10.1103/PhysRevE.96.052101. Epub 2017 Nov 1.
After constructing a formalism to analyze spatial stress correlations in two-dimensional equilibrated liquids, we show that the sole conjunction of mechanical balance and material isotropy demands all anisotropic components of the inherent state (IS) stress autocorrelation matrix to decay at long range as 1/r^{2} in the large system size limit. Furthermore, analyzing numerical simulation data for an equilibrated supercooled liquid, we bring evidence that, in finite-sized periodic systems, the autocorrelations of pressure and shear stresses present uniform backgrounds of amplitudes proportional to the inverse cell area. These backgrounds bring relevant contributions to macroscopic IS stress fluctuations, with the consequence that the latter scale as inverse area, yet in an anomalous way, inconsistent with viewing an IS as equivalent, in the thermodynamic limit, to an ensemble of independent finite-sized subsystems. In that sense, ISs are not spatially ergodic.
在构建了一种分析二维平衡液体中空间应力相关性的形式理论之后，我们表明，仅机械平衡和材料各向同性的结合就要求固有状态（IS）应力自相关矩阵的所有各向异性分量在大系统尺寸极限下以 1/r^{2}的方式长程衰减。此外，通过分析平衡过冷液体的数值模拟数据，我们提供了证据，表明在有限大小的周期性系统中，压力和剪切应力的自相关呈现出与单元面积成反比的幅度均匀背景。这些背景对宏观 IS 应力波动有重要贡献，其结果是，后者按面积的倒数缩放，但以一种异常的方式，与将 IS 视为在热力学极限下等同于独立的有限大小子系统的观点不一致。从这个意义上说，IS 不是空间遍历的。
