Hydrodynamic limits of Ginzburg-Landau vortices

Many quantum physical systems (for example superconductors, superfluids, Bose-Einstein condensates) exhibit vortex states that can be described by Ginzburg-Landau type functionals. For various equations of motion for the physical systems, the dynamical behaviour of finite numbers of vortices has been rigorously established. In a superconductor, one typically has millions of vortices, and so it is necessary to work with the vortex density instead of individual vortices. This leads to hydrodynamic evolution equations that are dissipative relatives of the Euler equations of incompressible fluids.

There are several interesting directions to pursue here, for example, to understand how vortex dynamics is related to the surprising sign change of the Hall effect in some superconductors. There are also numerous analogies to fluid dynamics to study.

The PhD student will work on a problem that has connections to the calculus of variations, to partial differential equations and to fluid mechanics, and should have some experience in one of these fields.

Apply: This studentship is open now and will be available until it is filled. To apply please visit the University Of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx