Infinite Network of Identical Capacitors by Green's Function

TL;DR

This paper calculates the capacitance between nodes in infinite networks of identical capacitors using Green's functions, revealing asymptotic behaviors and connections to lattice properties.

Contribution

It introduces a Green's function approach to compute capacitance in infinite capacitor networks, applicable to various lattice structures.

Findings

Capacitance between nodes can be calculated using Green's functions.

Asymptotic behavior of capacitance is characterized for large separations.

Relation established between lattice capacitance and van Hove singularities.

Abstract

The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l,m)for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the lattice green's function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for large separation between the origin and the site (l,m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight- binding Hamiltonian. This method can be applied to other types of lattice structures.