The Little-Parks Effect in an Inhomogeneous Superconducting Ring

An inhomogeneous superconducting ring (hollow cylinder) placed in a magnetic field is considered. It is shown that the superconducting transition of the section with the lowest critical temperature may be a first order phase transition if the magnetic flux contained within the ring is not divisible by the flux quantum. In the vicinity of this transition, thermal fluctuations can induce the voltage in the ring with rather small sizes.