C05 Numerical approximation of the Gross-Pitaevskii equation via vortex tracking

Gross-Pitaevskii equations play a central role in various models of condensed matter physics. A dominating feature is the occurrence of quantized vortices that effectively evolve according to a Hamilton-ODE system. The project aims at placing the well-developed analytical theory of this singular limit in a computational framework that allows to prove accuracy and efficiency of numerical approximations throughout the vortex regime ε ≪ 1. Equipped with these simulation tools, we expect to gain new analytical insights, for example on complex periodic solutions of the Gross-Pitaevskii equation.