Random Walks through the Ensemble: Linking Spectral Statistics with Wave-Function Correlations in Disordered Metals

We use a random walk in the ensemble of impurity configurations to generate a Brownian motion model for energy levels in disordered conductors. Treating arclength along the random walk as fictitous time, the resulting Langevin equation relates spectral statistics to eigenfunction correlations. Solving this equation al energy scales large compared with the mean level spacing, we obtain the spectral form factor and its parametric dependence.