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 acattering.The junction is expressed by a 4×4S-matrix,which is very similar to that used by Buttiker in sequential tunnelling.Since the S-matrix is unitary,the current conservation keeps antomatically,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 a 3×3 matrix.