Periodic orbit theory and spectral statistics for scaling quantum graphs

英文摘要：

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, $δk_{n}=k_{n}-\bar k_{n}$.