VARIATIONAL APPROACH TO SUPERCONDUCTIVE NETWORKS

An approach to superconductive micronetworks is presented that makes u se of the currents in the loops and the order parameter along branches as fundamental variables. Fluxoid quantization is introduced as a con straint and inductive effects are explicitly taken into account. The t heory is made the starting point of a variational formulation which ca n use any physically sound guess for the order parameter as a trial fu nction to minimize the free energy. For second-order transitions the z eroth-order approximation of de Gennes and Alexander can be used as a trial function. The formalism allows for the amplitude of the order pa rameter to be determined as a function of temperature and field. A dif ferent choice of ansatz allows the theory to describe transitions taki ng place when external currents are fed. In this paper we apply the ne w method to some systems, including a superconducting interferometer w ithout Josephson junctions. The results compare quite well with experi ments as well as with exact numerical calculations, giving a fair desc ription of these systems.