Quantum diffusion and divergent fluctuations in disordered metals

The aim of this paper is to pin down the physical origin of the logarithmic divergences predicted by recent theories of conduction in disordered two-dimensional metals. Using an intuitive argument, we show that a simple a priori estimate of corrections to the Boltzmann equation yields logarithmic corrections to the conductivity. A nonperturbative calculation establishes a direct link between diffusion processes and logarithmic singularities in microscopic properties such as the local density of states. Finally, fluctuations in the linear response to an electric field are calculated in perturbation theory. They are shown to diverge in four or fewer dimensions, possibly indicating a breakdown of perturbation theory.