Theory of resistor networks: The two-point resistance
Mathematical Physics
2009-11-10 v2 Materials Science
math.MP
Probability
Physics Education
Abstract
The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.
Cite
@article{arxiv.math-ph/0402038,
title = {Theory of resistor networks: The two-point resistance},
author = {F. Y. Wu},
journal= {arXiv preprint arXiv:math-ph/0402038},
year = {2009}
}
Comments
30 pages, 5 figures now included; typos in Example 1 corrected