Equivalence of the multilead approach to dephasing and the self-consistent Born approximation

We show that the resistance in a multiprobe geometry with dephasing leads is the same as the resistance of the same multiprobe geometry without dephasing leads but in the presence of a two-body interaction in the self-consistent Born approximation. The interaction used is local and elastic. This is an exact mapping between the two methods for introducing dephasing. The calculation is performed at zero temperature and magnetic field. We give a recursive algorithm for computing the conductance matrix elements in the presence of dephasing. The algorithm is similar to the usual recursive Green’s-function method except that the matrices are ${\mathit{n}}^2$×${\mathit{n}}^2$ matrices rather than n×n matrices, where n is the width of the wire.