Thermal fluctuations of the Josephson current in a ring of   superconducting grains
  Thermal fluctuations of the Josephson current $I$ induced by the magnetic flux through a ring of $N$ superconducting grains are studied. When a half-fluxon is threading the ring, $I$ exhibits incoherent transitions between the two degenerate states due to thermal phase slips. We propose a new numerical method to deal with both equilibrium and dynamic properties of Josephson systems. Computed transition rate has the form $\Gamma = A(N)\exp[-B(N)/T]$, where $B(N)$ agrees with the analytical result derived for the energy barrier associated with phase slips. In the non-degenerate case (e.g., at a quarter-fluxon) the equilibrium value of $I$ decreases with $T$ due to harmonic excitations and then gets destroyed by phase slips. 
D. A. Garanin and E. M. Chudnovsky
cond-mat.supr-con