  We present experimental and numerical results for the long-range fluctuation
properties in the spectra of quantum graphs with chaotic classical dynamics and
preserved time-reversal invariance. Such systems are generally believed to
provide an ideal basis for the experimental study of prob- lems originating
from the field of quantum chaos and random matrix theory. Our objective is to
demonstrate that this is true only for short-range fluctuation properties in
the spectra, whereas the observation of deviations in the long-range
fluctuations is typical for quantum graphs. This may be attributed to the
unavoidable occurrence of short periodic orbits, which explore only the
individual bonds forming a graph and thus do not sense the chaoticity of its
dynamics. In order to corrobo- rate our supposition, we performed numerous
experimental and corresponding numerical studies of long-range fluctuations in
terms of the number variance and the power spectrum. Furthermore, we evaluated
length spectra and compared them to semiclassical ones obtained from the exact
trace formula for quantum graphs.
