论文标题
格林的随机电阻网络功能
Green's Functions For Random Resistor Networks
论文作者
论文摘要
我们通过研究格林在任意维度中的功能来分析随机电阻网络。我们开发系统的疾病扰动扩展，以描述这种系统的弱混乱状态。我们使用此公式以层次的方式计算合奏平均的节点电压和键电电流。我们通过直接对平方晶格的直接数值模拟来验证该扩展的有效性，每个键在每个键上分布时都具有电阻。此外，我们构建了一种形式主义，以递归地获得有限的许多无序键的绿色功能。我们为具有多达四个无序键的晶格提供明确的表达式，可用于预测淋巴结分布，以实现任意较大的混乱强度。最后，我们引入了一个新颖的订单参数，该参数衡量了给定的电阻构型，该参数衡量了粘结电流和最佳路径（电阻最小的路径）之间的重叠，这有助于表征系统的弱和强障碍状态。
We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation to compute ensemble averaged nodal voltages and bond currents in a hierarchical fashion. We verify the validity of this expansion with direct numerical simulations of a square lattice with resistances at each bond exponentially distributed. Additionally, we construct a formalism to recursively obtain the exact Green's functions for finitely many disordered bonds. We provide explicit expressions for lattices with up to four disordered bonds, which can be used to predict nodal voltage distributions for arbitrarily large disorder strengths. Finally, we introduce a novel order parameter that measures the overlap between the bond current and the optimal path (the path of least resistance), for a given resistance configuration, which helps to characterize the weak and strong disorder regimes of the system.
