GAUSSIAN RANDOM-MATRIX PROCESS AND UNIVERSAL PARAMETRIC CORRELATIONS IN COMPLEX-SYSTEMS

We introduce the framework of the Gaussian random-matrix process as an extension of Dyson's Gaussian ensembles and use it to discuss the sta tistical properties of complex quantum systems that depend on an exter nal parameter. We classify the Gaussian processes according to the sho rt-distance diffusive behavior of their energy levels and demonstrate that all parametric correlation functions become universal upon the ap propriate scaling of the parameter. The class of differentiable Gaussi an processes is identified as the relevant one for most physical syste ms. We reproduce the known spectral correlators and compute eigenfunct ion correlators in their universal form Numerical evidence from both a chaotic model and weakly disordered model confirms our predictions.