Günter Rote:

Characterization of the response maps of alternating-current networks

Manuscript, April 2019, 6 pages, arXiv:1904.02031 [math.CO], submitted for publication.  →BibTeX


An alternating-current network is an undirected graph in which each edge is weighted by a conductance, a complex number with positive real part. Some nodes are designated as boundary nodes. The response map is the linear map from the vector of voltages at the boundary nodes to the vector of currents flowing into the network through these nodes.

We prove that the known necessary conditions for a linear map to be a response map are sufficient, and we show how to construct an appropriate alternating-current network for a given response map.

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Last update: April 4, 2019.