Fluctuation statistics for quantum star graphs

Star graphs are examples of quantum graphs in which the spectral and eigenfunction statistics can be determined exactly and explicitly. They show behaviour intermediate between that expected for quantum chaotic systems and that expected for integrable systems. I review here the main results relating to star graphs in the context of our general understanding of the statistical properties of quantum systems in the semiclassical limit. In particular, I focus on recent results concerning quantum ergodicity and scarring in the eigenfunctions.

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