Spectral statistics of nondiffusive disordered electron systems: A comprehensive approach.

Abstract

We present an analysis of the two-level correlation function (K) and the fluctuation of the level number (${\mathrm{\ensuremath{\Sigma}}}_{2}$) within an energy interval E of disordered conductors. Our analysis extends to nondiffusive regimes, including E larger than the inverse elastic scattering time \ensuremath{\Elzxh}/\ensuremath{\tau} and ballistic (but not perfectly clean) systems. Technically, our perturbational approach goes beyond the common diffusion and cooperon approximation. We find additional types of behavior for K and ${\mathrm{\ensuremath{\Sigma}}}_{2}$. These manifest in the large-energy (E>\ensuremath{\Elzxh}/\ensuremath{\tau}) nonuniversal regime, which is studied vis-\`a-vis general features of the scattering potential. The impurity-averaged correlation function is contrasted with energy-averaged correlators often employed in the context of quantum chaos. Various composite correlation functions, defined with respect to energy, disorder, and possibly sample-size-averaging procedures, are introduced and calculated. This provides a bridge between the physics of clean chaotic and disordered systems. We extend our analysis to the case of an external magnetic field that is applied to a diffusive sample. We address the question of how strong magnetic fields, corresponding to magnetic lengths smaller than the elastic mean free path, affect the spectral statistics.