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In mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected by bonds (or edges) with a differential or pseudo-differential operator acting on functions defined on the bonds. Such systems were first studied by Linus Pauling as models of free electrons in organic molecules in the 1930s. They arise in a variety of mathematical contexts, e.g. as model systems in quantum chaos, in the study of waveguides, in photonic crystals and in Anderson localization, or as limit on shrinking thin wires. Quantum graphs have become prominent models in mesoscopic physics used to obtain a theoretical understanding of nanotechnology. Another, more simple notion of quantum graphs was introduced by Freedman et al.〔M. Freedman, L. Lovász & A. Schrijver, Reflection positivity, rank connectivity, and homomorphism of graphs, (''J. Amer. Math. Soc.'' 20, 37-51 (2007) ); (MR2257396 )〕 == Metric graphs == A metric graph is a graph consisting of a set of vertices and a set of edges where each edge has been associated with an interval so that is the coordinate on the interval, the vertex corresponds to and to or vice versa. The choice of which vertex lies at zero is arbitrary with the alternative corresponding to a change of coordinate on the edge. The graph has a natural metric: for two points on the graph, is the shortest distance between them where distance is measured along the edges of the graph. Open graphs: in the combinatorial graph model edges always join pairs of vertices however in a quantum graph one may also consider semi-infinite edges. These are edges associated with the interval attached to a single vertex at . A graph with one or more such open edges is referred to as an open graph. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quantum graph」の詳細全文を読む スポンサード リンク
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