The Ginzburg-Landau model serves as a basic paradigm for a broad spectrum of subjects in pattern-forming systems in general and in superconductivity in particular. The investigator studies several fundamental theoretical problems related to this model. Some of the specific problems that he examines lie at the heart of the Ginzburg-Landau formalism. These include the understanding of time-dependent formulation and of thermal fluctuations, together with the elucidation of the behavior of superconductors near the sample's boundary. Other problems studied are related to transport phenomena in thin wires with Joesphson junctions. Such structures are crucial in several basic superconducting devices. The investigator suggests a research direction that leads to the introduction of novel junctions. Finally, he analyzes the existence of stable patterns in different systems (including liquid crystals and superconductors with impurities) where the stability is not generated by an acting external force, but by the topology of the sample.
One aspect of the project is to enhance the fundamental understanding of superconductivity. A second aspect of this project is to study transport in extremely narrow networks. While the main motivation is to consider such transport processes in superconductors, these types of problems are relevant to many areas. For example, quantum wires are among the current leading models for quantum computers, microchannel chips are developing into fast and efficient tools in chemical analysis, etc. The work in this area will have an impact on certain directions in nanotechnology. A major theme of the project is to exploit the similarity between the mathematical methods used in different applications, such as optics, liquid crystals, and superconductivity, in order to apply techniques developed in one of these areas to another one.
