Persistent current in thin superconducting wires

In this paper, we explore the persistent current in thin superconducting wires and accurately examine the effects of the phase slips on that current. The main result of the paper is the formula for persistent current in terms of solutions of certain (nonlinear) integral equation. This equation allows to find asymptotics of the current at long(small) length of the wire, in this paper, we examine the region in which the system becomes strongly interacting and very few pieces of information can be extracted by perturbation theory. Nevertheless, due to the integrability, exact results for the current can be obtained. We observe that at the limit of a long wire, the current becomes exponentially small and we believe that it is the signal that phase slips may destroy superconductivity for long wires, below BKT phase transition. (paper)