  We explore the influence of an arbitrary external potential perturbation V on
the spectral properties of a weakly disordered conductor. In the framework of a
statistical field theory of a nonlinear sigma-model type we find, depending on
the range and the profile of the external perturbation, two qualitatively
different universal regimes of parametric spectral statistics (i.e.
cross-correlations between the spectra of Hamiltonians H and H+V). We identify
the translational invariance of the correlations in the space of Hamiltonians
as the key indicator of universality, and find the connection between the
coordinate system in this space which makes the translational invariance
manifest, and the physically measurable properties of the system. In
particular, in the case of localized perturbations, the latter turn out to be
the eigenphases of the scattering matrix for scattering off the perturbing
potential V. They also have a purely statistical interpretation in terms of the
moments of the level velocity distribution. Finally, on the basis of this
analysis, a set of results obtained recently by the authors using random matrix
theory methods is shown to be applicable to a much wider class of disordered
and chaotic structures.
