Theory of the Residual Resistivity Dipole. Flow of Non‐Interacting Particles under a Weak Driving Force around a Fixed Point Scatterer

Employing a superposition representation of the density matrix the perturbation of the stationary current flow by a fixed point scatterer is treated approximately. The current is driven by a weak constant force. The problem, the method, and the result parallel closely those of the corresponding force‐free diffusion case discussed previously. For all current‐proportional perturbation terms, the Einstein equivalence between a force and a density gradient is established for the inhomogeneous case under study. This equivalences, however, is broken by an additional current‐free term of the density matrix. This term can be identified as a relict of the inhomogeneous equilibrium state in the given static force field. This equilibrium state itself is also studied. In the ensemble the limitations of the concept of a local chemical potential become evident, even in the current‐free state.