The investigator studies several fundamental theoretical problems of superconductivity. Through analysis of the time-dependent Ginzburg-Landau model, he examines: 1. Critical currents, and bounds on them, associated with the loss of stability of the normal and superconducting states in two and three dimensions. 2. Phase transitions between these states in various circumstances. 3. Critical currents under magnetic field effects near the normal state. 4. Highly nonlinear effects of induced magnetic fields.
Superconductors are metals that at a sufficiently low temperature exhibit two important properties: 1. They lose entirely their electrical resistivity. 2. The magnetic field is excluded from the superconducting area. Superconductors have great technological potential for applications ranging from magnetic sensors, through generators of large magnetic fields, to high power transmitters. The investigator studies the behavior of superconducting materials near the critical current, the maximum current density which can flow through a superconducting wire with (practically) zero resistance. He focuses on the transition between the normal and superconducting states, how stable these states are, and effects of induced magnetic fields on the critical current. Of particular interest is the disparity between experimental measures of the critical current and theoretical predictions of the critical current in the absence of magnetic fields. Determining the maximal current a superconductor can carry before reverting to the normal state where material resistivity causes energy losses is an important consideration in superconductor technologies. The project sheds light on both the nucleation of superconductivity for decreasing currents, and on the loss of superconducting properties when the electric current increases.