By Avron J.E.

The adiabatic quantum delivery in multiply hooked up structures is tested. The platforms thought of have numerous holes, often 3 or extra, threaded via self reliant flux tubes, the delivery houses of that are defined by way of matrix-valued features of the fluxes. the most topic is the differential-geometric interpretation of Kubo's formulation as curvatures. due to this interpretation, and since flux area may be pointed out with the multitorus, the adiabatic conductances have topological value, relating to the 1st Chern personality. specifically, they've got quantized averages. The authors describe quite a few periods of quantum Hamiltonians that describe multiply attached structures and examine their simple houses. They pay attention to versions that decrease to the learn of finite-dimensional matrices. specifically, the aid of the "free-electron" Schrödinger operator, on a community of skinny wires, to a matrix challenge is defined intimately. The authors outline "loop currents" and examine their houses and their dependence at the number of flux tubes. They introduce a mode of topological type of networks in response to their delivery. This results in the research of point crossings and to the organization of "charges" with crossing issues. Networks made with 3 equilateral triangles are investigated and categorised, either numerically and analytically. a lot of those networks end up to have nontrivial topological delivery homes for either the free-electron and the tight-binding types. The authors finish with a few open difficulties and questions.

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