Thermal fluctuations of the Josephson current in a ring of superconducting grains

Thermal fluctuations of the Josephson current 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. In this study, we propose a numerical method to deal with both equilibrium and dynamic properties of Josephson systems. Computed transition rate has the form Γ = 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 nondegenerate 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.