PERSISTENT CURRENTS IN HIGH DIMENSIONS

We introduce a model for the persistent current carried by spinless fe rmions moving in a ring with a high-dimensional cross section. The eff ects of both disorder and electron-electron interaction are considered . It is found that the non-interacting system behaves like previously considered low-dimensional models. The more complicated interacting/di sordered case is analysed by means of a functional integral which is e valuated in the limit of infinite dimensionality by expanding in the n umber of transverse channels. To leading order in this expansion schem e, the Coulomb interaction does not affect the persistent current. It is found that the insensitivity to interaction effects is due to the a bsence of local contributions to the Coulomb vertex in our model (whic h in turn is a consequence of the neglect of the electron spin). It is argued that the physical mechanism suppressing the interaction in the high-dimensional spinless model applies to the analogous low-dimensio nal case as well.