Numerical exploration of vortex matter in Bose-Einstein condensates

We describe a finite element numerical approach to the full Hartree-Fock-Bogoliubov treatment of a vortex lattice in a rapidly rotating Bose-Einstein condensate. We study the system in the regime of high thermal or significant quantum fluctuations where we are presented with a very large nonlinear unsymmetric eigenvalue problem which is indefinite and which possesses low-lying excitations clustered arbitrarily close to zero, a problem that requires state-of-the-art numerical techniques.