The adiabatic quantum transport in multiply connected systems is examined. The systems considered have several holes, usually three or more, threaded by independent flux tubes, the transport properties of which are described by matrix-valued functions of the fluxes. The main theme is the differential-geometric interpretation of Kubo's formulas as curvatures. Because of this interpretation, and because flux space can be identified with the multitorus, the adiabatic conductances have topological significance, related to the first Chem character. In particular, they have quantized averages. The authors describe various classes of quantum Hamiltonians that describe multiply connected systems and investigate their basic properties. They concentrate on models that reduce to the study of finite-dimensional matrices. In particular, the reduction of the "free-electron" Schrodinger operator, on a network of thin wires, to a matrix problem is described in detail. The authors define "loop currents" and investigate their properties and their dependence on the choice of flux tubes. They introduce a method of topological classification of networks according to their transport. This leads to the analysis of level crossings and to the association of "charges" with crossing points. Networks made with three equilateral triangles are investigated and classified, both numerically and analytically. Many of these networks turn out to have nontrivial topological transport properties for both the free-electron and thy tight-binding models. The authors conclude with some open problems and questions.
The dichromate‐wet combustion determination of soil organic matter involves a titration of the excessive dichromate. A potentiometric titration is proposed. This modification enables a fast and accurate and point determination. Moreover, the method can be easily adapted for automatic titrations.
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