Scattering approach to persistent currents in infinitely extended quantum systems

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Abstract
The scattering approach leading to a statistical theory for the transfer matrix is used to study the persistent currents in a disordered mesoscopic ring threaded by a magnetic flux and connected to a semi-infinite wire. The S matrix of the system is found for a two-dimensional (2D) configuration in terms of the scattering matrix of the junction connecting the ring with the wire and the scattering or the transfer matrix of the ring. A detailed analysis is performed for 1D conductors. The role of the S-matrix poles in determining the current is studied. When the chemical potential is kept fixed, the statistical average of the persistent current is calculated and, in the range explained in the text, is expressed as a series expansion valid for arbitrary disorder and thus represents the general solution of our problem, for 1D conductors.