Screening in clean mesoscopic rings

The dielectic function for electrons restricted to move on a clean one-dimensional ring is calculated in the random-phase approximation (RPA) and used for the computation of the Coulomb interaction energy. As a possible application we consider the situation in which the ring is threaded by a magnetic flux. It is found that the Coulomb energy does not depend on the magnetic flux (although the dielectric function does). This result confirms (within the RPA) the conjecture that in one-dimensional clean rings, the Coulomb interaction does not affect the persistent current of a noninteracting electron gas.