Periodic orbit theory and spectral statistics for scaling quantum graphs

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, $\delta k_n=k_n-{\bar{k}}_n$.

24 pages, 5 figures