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Periodic orbit theory and spectral statistics for scaling quantum graphs

Yu. Dabaghian
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Abstract

The explicit solution to the spectral problem of quantum graphs found recently in \cite{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, $s_{n}=k_{n}-k_{n-1}$, and the distribution of the spectral oscillations around the average, $δk_{n}=k_{n}-\bar k_{n}$.

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Yu. Dabaghian. 2007-01-18. Periodic orbit theory and spectral statistics for scaling quantum graphs. https://arxiv.org/abs/quant-ph/0701128

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