Finite-size effects in a metallic multichannel ring with Kondo impurity: Persistent currents and magnetoresistance

We consider a spin-1/2 impurity interacting with conduction electrons in two different orbital channels via an isotropic spin exchange. The exchange is the same for both channels, but a crystalline held breaks the symmetry between the orbital channels. This corresponds to a splitting of the conduction electron Gamma(8) into two doublets in the quadrupolar Kondo effect, or to the electron-assisted tunneling of an atom in a double-well potential in an external magnetic field. Another possible realization could be a quantum dot coupled to two equal rings of the same length subject to an electrostatic potential difference. We consider the Bethe ansatz equations for this model and derive the tower structure of the finite size corrections to the ground-state energy. These results are used to discuss the Aharonov-Bohm-Casher interference pattern in the persistent charge and spin currents, and the magnetoresistivity due to the scattering of electrons off the impurity.