In Heidelberg I was working a PhD student and Postdoc on Bose-Einstein condensates, in particular on
methods to obtain variationally optimal solutions of the many-body Schrödinger equation.
Thereby, we could provide numerically exact solutions of the time-dependent many-boson Schrödinger equation using the
of which I am a developer.
We also invented variationally
optimal lattice models, i.e. lattice models that are based
entirely on the principle of least action. These provide a great computational advantage over conventional
lattice models. We showed this by comparing the Bose-Hubbard
model to the variationally optimal Bose-Hubbard model.
A while ago, we investigated the ground state of the Lieb-Liniger system as a model for a Bose-Einstein condensates on a ring.