Dynamic transitions between metastable states in a superconducting ring

Abstract

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.