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. © 2009 IMACS.
Baksmaty, L. O., Liu, Y., Landman, U., Bigelow, N. P., & Pu, H. (2009). Numerical exploration of vortex matter in Bose-Einstein condensates. Mathematics and Computers in Simulation, 80(1), 131–138. https://doi.org/10.1016/j.matcom.2009.06.011