Event № 285
I will introduce the Ginzburg-Landau (GL) equations and give a very brief discussion of solutions with a single vortex per lattice cell. The focus of this talk, however, will be on the general case of multi-vortex solutions. We attempt to bifurcate a branch of such solutions from the normal state solution with constant magnetic field. A main difficulty is the reduction of dimension of solutions of the linearized problem. One can transfer this problem onto a suitable space of theta functions and use more algebraic methods to study the problem. I will discuss low flux (per lattice cell) results and give a brief sketch of the proof by exploiting symmetries of the underlying Abrikosov lattice.