Dynamic transitions between metastable states in a superconducting ring
  Applying the time-dependent Ginzburg-Landau equations, transitions between metastable states of a superconducting ring are investigated in the presence of an external magnetic field. It is shown that if the ring exhibits several metastable states at a particular magnetic field, the transition from one metastable state to another one is governed by both the relaxation time of the absolute value of the order parameter tau_{|psi|} and the relaxation time of the phase of the order parameter tau_{phi}. We found that the larger the ratio tau_{|psi|}tau_{phi} the closer the final state will be to the absolute minimum of the free energy, i.e. the thermodynamic equilibrium. The transition to the final state occurs through a subsequent set of single phase slips at a particular point along the ring. 
D.Y. Vodolazov and F.M. Peeters