Driving forces for electromigration by linear response

We examine the driving forces acting on an electromigrating atom through a linear-response formalism, extending the analysis of Kumar and Sorbello. With the aid of a formal transformation we can cast the result for the force on a certain atom in terms of an expression which may be interpreted as the contribution to the resistivity due to that atom. This interpretation is independent of scattering strength or screening extent. For a simple model system we reduce our formal expression to results that may be easily evaluated. Particular care is given to the approximations required in this model reduction. The final formulas reproduce various standard results, while the general derivation allows a different and useful point of view on the problem.