Discrete Green's Functions and Functional Determinants

Arnold, J.M. (2017) Discrete Green's Functions and Functional Determinants. In: International Conference on Electromagnetics in Advanced Applications (ICEAA 2017), Verona, Italy, 11-15 Sep 2017, pp. 1072-1075. ISBN 9781509044511 (doi: 10.1109/ICEAA.2017.8065447)

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Abstract

A theorem is shown in which the elements of the inverse of a symmetric matrix F are constructed by Jacobi's formula using the derivative of the determinant detF with respect to its elements, and the determinant is defined by the partition function of a statistical field theory with interaction matrix F, generally Z = (detF)-1/2. When the matrix F is the discrete Laplacian, the theorem is the essential connection between the discrete Green's function and two-point correlations of the lattice gas.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Arnold, Professor John
Authors: Arnold, J.M.
College/School:College of Science and Engineering > School of Engineering
ISBN:9781509044511

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