论文标题
无限维粒子系统的平均场动力学：全局剪切与随机局部强迫
Mean-field dynamics of infinite-dimensional particle systems: global shear versus random local forcing
论文作者
论文摘要
在无限的尺寸中，成对相互作用粒子的多体系统为无定形材料的特征（例如，在准息剪切下的玻璃的应力 - 应变曲线）提供了精确的分析基准。在这里，我们考虑了一种替代驾驶协议，而不是全球剪切，如前所述。 [1]，包括在每个粒子上随机分配一个恒定的局部位移，并具有有限的空间相关长度。我们表明，在无限尺寸限制下，在这种随机强迫下的平均场动力学严格等同于在累积菌株的简单重新缩放后，在全球剪切下等效。此外，缩放因子基本上是由相互作用对粒子的相对局部位移的方差给出的，该方差编码有限的空间相关性。在此框架中，全球剪切只是一个更广泛的本地强迫系列的特殊情况，可以通过调整其空间相关性来探索。我们特别讨论了对玻璃的绝对驾驶的含义 - 最初以复制对称平衡制备 - 以及如何将相应的“应力 - 应变”曲线和弹性模量重新降低到其准持近式切片上。这些结果暗示了一个统一的框架，用于在不同驱动的无序系统之间在平均场水平上建立严格的类比。
In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol as recently introduced in Ref. [1], which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the infinite-dimension limit, the mean-field dynamics under such a random forcing is strictly equivalent to that under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements on interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. We discuss specifically the implications on the quasistatic driving of glasses -- initially prepared at a replica-symmetric equilibrium -- and how the corresponding 'stress-strain'-like curves and the elastic moduli can be rescaled onto their quasistatic-shear counterparts. These results hint at a unifying framework for establishing rigourous analogies, at the mean-field level, between different driven disordered systems.
