Resistance Calculation for an infinite Simple Cubic Lattice- Application of Green's Function

TL;DR

This paper derives a rational expression for electrical resistance between points in an infinite simple cubic lattice using Green's functions, and explores effects of lattice perturbations and asymptotic resistance behavior.

Contribution

It introduces a method to calculate resistances in an infinite cubic lattice and analyzes the impact of removing resistors and the asymptotic resistance behavior.

Findings

Resistance expressed rationally in terms of G0(0,0,0)

Resistance behavior studied when a resistor is removed

Asymptotic resistance behavior analyzed

Abstract

It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) is expressed rationally in terms of the known value of G0(0,0,0). The resistance between arbitrary sites in a SC is also studied and calculated when one of the resistors is removed from the perfect lattice. Finally, the asymptotic behavior of the resistance for both the perfect and perturbed SC network is investigated