Families of line-graphs and their quantization

Details Families of line-graphs and their quantization Families of line-graphs and their quantization

2001-10-23

arxiv.org/abs/nlin/0110043v2

J. Stat. Phys. 111 (2003) 1331

Nonlinear Sciences

Chaotic Dynamics

LaTeX 17 pages, 9 figures included, v2: additional co-author, new chapter with analythical results on quantizable digraphs add

Scientific paper

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L^n(G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.

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