Periodic orbit theory and spectral statistics for scaling quantum graphs
Abstract
The explicit solution to the spectral problem of quantum graphs found recently in Anima, is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations, sn=kn-kn-1, and the distribution of the spectral oscillations around the average, δ kn=kn- kn.
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