Lattice Green/Neumann function for the 2D Laplacian operator defined on square lattice on cylinders, tori and other geometries with some applications

DOI10.1088/1751-8121/accfd5MaRDI QIDQ6046091

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Publication date: 15 May 2023

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

zbMATH Keywords

method of imagessimple random walkdiscrete Neumann problemlattice Green functiontwo-point resistanceflat square lattice

Mathematics Subject Classification ID

Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

Cites Work

• Fundamental solution of the Laplacian on flat tori and boundary value problems for the planar Poisson equation in rectangles
• Discrete scattering theory: Green's function for a square lattice
• The electrical resistance of a graph captures its commute and cover times
• Discrete potential theory
• Theory of resistor networks: the two-point resistance
• Lattice Green's functions in all dimensions
• The Dirichlet to Neumann Map for a Resistor Network
• Statistical Field Theory
• Lattice discretization in quantum scattering
• Series expansions for lattice Green functions
• INFINITE NETWORKS OF IDENTICAL CAPACITORS
• Lattice Green's Function. Introduction
• Theory of impedance networks: the two-point impedance andLCresonances
• The exact evaluation of the corner-to-corner resistance of anM×Nresistor network: asymptotic expansion
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