Gaussian processes and universal parametric decorrelations of wavefunctions

Gaussian processes that depend on a parameter lead to universal parametric correlations of spectra and wavefunctions after an appropriate scaling of the parameter. The most general Gaussian process is described by the exponent eta which characterizes the diffusive behavior of its energy levels. We discuss the scaling required for such processes and show that they lead to the same parametric correlators when considered as functions of (Delta (x) over bar)(eta/2) where (x) over bar is the scaled parameter. Using simulations of Gaussian processes, we demonstrate this scaling and universality for the parametric decorrelation of the wavefunctions as measured by their overlap, and compute the respective distributions of that overlap.