2004/02/19 by F Y Wu, F. Y. Wu · 7 citations
Materials Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Combinatorics #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Graph theory and applications #Laplace operator #Laplacian matrix #Markov Chains and Monte Carlo Methods #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Point (geometry) #Pure mathematics #Quantum mechanics #Quasicrystal Structures and Properties #Resistor #Topology (electrical circuits) #cond-mat.mtrl-sci #math-ph #math.MP #math.PR #physics.ed-ph
paper · pdf · doi:10.1088/0305-4470/37/26/004
published as Journal of Physics A 37, 6653-6673 (2004) · 30 pages, 5 figures now included; typos in Example 1 corrected
arxiv created 2004/02/19 · openalex publication_date 2004/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Möbius 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 analyse large-size expansions in two and higher dimensions.