Non-perturbative evaluation of the static electrical conductivity for disordered systems

A non-perturbative, representation-independent method of studying the linear response of a disordered system to an external field is presented. For a homogeneous system, the momentum space representation of the basic equations reproduces Van Hove's results. This method is applied to evaluate the static conductivity of a disordered system in the absence of a magnetic field. It is found that σ can be split into a portion proportional to the unit tensor, which is negligible in the weak coupling limit, and a second portion which exhibits the functional structure of the elementary expression one gets from the Boltzmann equation. In the strong coupling case, the first term may be important.