Models in Superconductivity

Indiana University, Bloomington IN

Investigators

Abstract

Proposal: DMS-0203312 PI: Jacob Rubinstein Institution: Indiana University Bloomington Title: Models in superconductivity ABSTRACT The project is aimed at developing a variety of models in superconductivity. The specific areas that are covered include mesoscopic networks, Josephson junctions, and time-dependent models. One of the goals is the derivation of specialized models in certain distinguished asymptotic limits. Another goal is to study the relation between the applied magnetic field and the resulting current distribution as a function of the geometry and the topology of the network. Superconductors form a special kind of material with the unique property that they exhibit quantum-mechanical (that is, atomic) effects on large scales that can be observed by the unaided eye. This makes them wonderful candidates to our understanding of the basic laws that govern atomic phenomena. It also makes them candidates for many applications ranging from very precise measuring devices and unusual generators of magnetic fields (already on the market) to quantum computers. To understand the behavior of superconductors we need mathematical models. Moreover, since the standard model is very complicated, it is very useful to derive simpler models that fit special circumstances. For example, some of the fascinating effects of superconductivity are observed when the material forms a complex network of thin wires. I therefore derive special models to describe such geometries.