Abstract : In a first part, some features of the propagation of an electron in
disordered media are studied by using the perturbation expansion
given by the Watson series. The use of finite range potentials
requires the introduction of off-energy-shell scattering matrix
elements, which allow to calculate analytically each element of the
series. Corrections to the Boltzmann mean free path in 2 and
3 dimensions are obtained by averaging the electron propagator. The
size of the scatterer plays an essential role.
The exact summation of the Watson series, written in a compact matrix form,
allows for a numerical study of the total cross section of the
disordered system. The latter shows an unexpected behavior at the
transition between the ballistic regime and the diffusive regime.
The second part is concerned with the transport of interacting
electrons in disordered systems. The disorder is taken into account
by a static impurity field. The use of field theoretical tools allows
for a non perturbative approach of these systems,
in which the electron-electron interaction may generate a
A new approach in the spirit of the renormalization group approach is
then used to derive flow equations describing the evolution of the
coupling constants of the interacting electron system. At the
one-loop approximation, these equations lead to the results given by
the perturbation theory (RPA).