  We investigate the spectral properties of a generalized GOE (Gaussian
Orthogonal Ensemble) capable of describing critical statistics. The joint
distribution of eigenvalues of this model is expressed as the diagonal element
of the density matrix of a gas of particles governed by the Calogero-Sutherland
Hamiltonian (C-S). Taking advantage of the correspondence between C-S particles
and eigenvalues, we show that the number variance of our random matrix model is
asymptotically linear with a slope depending on the parameters of the model.
Such linear behavior is a signature of critical statistics. This random matrix
model may be relevant for the description of spectral correlations of complex
quantum systems with a self-similar/fractal Poincar\'e section of its classical
counterpart. This is shown in detail for two examples: the anisotropic Kepler
problem and a kicked particle in a well potential. In both cases the number
variance and the $\Delta_3$-statistic is accurately described by our analytical
results.
