Improved Coupled Reservoir Model for Inelastic Scattering in One-Dimensional Mesoscopic Metal Rings

In order to strictly solve the problem of persistent current in one-dimensional mesoscopic metal rings, a model with a perfect ring coupled to an external reservoir by a four-lead junction is introduced to independently describe inelastic scattering. The junction is expressed by a 4 x 4 S-matrix, which is very similar to that used by Büttiker in sequential tunneling. Since the S-matrix is unitary, the current conservation keeps automatically. Since the quadruplet of the matrix problem can be reduced into two topologically separate doublets, it gives a simple and elegant method compared with the former description with 3 x 3 matrix.