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A fully-connected graph with four vertices and sixteen directed bonds.  

A fully-connected graph with four vertices and sixteen directed bonds.  

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For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits represented by diagrams with up to two self-intersections connected by up to four arcs and explain why all other dia...

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... for a general class of graphs is a complicated and tedious task [16]. Fortunately, the calculation simplifies considerably for a special case described below. In this section we restrict our attention to fully-connected graphs with N vertices and B = N 2 directed bonds, including a loop at each of the vertices. An example with N = 4 is shown in Fig. 4. We assume that the vertex-scattering matrices ...

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... In view of the Bohigas-Giannoni-Schmidt conjecture [10], this observation led to the investigation of quantum graphs as a model for quantum chaos. Additional results regarding convergence of spectral statistics to those of random matrix theory include [7,8,18,19,44], among others. ...
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