MYPAPERS

The mean free path is an essential characteristic length in disordered systems. In microscopic calculations, it is usually approximated by the classical value of the elastic mean free path. It corresponds to the Boltzmann mean free path when only isotropic scattering is considered, but it is different for anisotropic scattering. In this paper, we work out the corrections to the so called Boltzmann mean free path due to multiple scattering effects on finite size scatterers, in the s-wave approximation, i.e. when the elastic mean free path is equivalent to the Boltzmann mean free path. The main result is the expression for the mean free path expanded in powers of the perturbative parameter given by the scatterer density.

A simple model is presented for the calculation of the quenched average over impurities which are rendered static by setting their mass equal to infinity. The path integral formalism of the second quantized theory contains annealed averages only. The similarity with the Gaussian quenched potential model is discussed.

An effective theory is suggested for the particle-anti particle and the particle-particle modes of strongly disordered electron systems. The effective theory is studied in the framework of the saddle point expansion and found to support a vacuum which is not invariant under translations in imaginary time. The Goldstone bosons of this symmetry breaking generate a pole in the density-density correlation function. The condensate of the auxiliary field corresponding to the particle-particle channel produces conductivity without relying on the long range fluctuations. The results are obtained for d>1.

A non-perturbative scheme, based on the functional generalization of the Callan-Symanzik equation is developed to treat the Coulomb interaction in an electron gas. The one-particle irreducible vertex functions are shown to satisfy an evolution equation whose initial condition is given by means of the classical action and the final point corresponds to the physical system. This equation is truncated by expanding it in momenta and excitation energies, leaving the electric charge as an arbitrary, not necessarily small parameter. Exact coupled partial differential equations up to first order in the frequencies and excitation energies are derived. The numerical integration of these equations is left to a later stage. Nevertheless, in order to demonstrate the relation with the perturbation expansion the one-loop Lindhard function and screening are reproduced in the independent mode approximation of the evolution equation.