Jens Bolte

Interacting many-particle quantum graphs

Quantum graphs are well established models in many areas of both Physics and Mathematics. While much work has been done on single-particle models, we will consider the construction of models of many interacting particles on the edges of a compact metric graph. We will establish basic spectral properties and show that in some very specific cases eigenfunctions can be represented using a Bethe ansatz. We will also discuss Bose-Einstein condensation in non-interacting systems as well as in some interacting cases.