Electromagnetic Properties of Mesoscopic Cylinder

The electromagnetic response of a mesoscopic cylinder made of a normal metal or a semiconductor is studied. The relation between the induced current J(q,w) and the electric field E(q,w) is derived. It is shown that the kernel K(q,w) which determines the properties of the system has a finite limit which implies infinite conductivity. The mesoscopic cylinder by virtue of its topology and small dimensions can support a persistent current. If the coherence of currents from different channels is strong enough a novel effect - the self-sustaining current can be obtained. We show that a mesoscopic multichannel system exhibits some features which bear resemblance to the superconductor.