Interacting many-particle systems and Bose-Einstein condensation on quantum graphs
Joachim Kerner,
(Royal Holloway, University of London)
Lunes 17 de septiembre 2012
In recent years quantum graphs have become important models
in the field of quantum chaos. So far, however, most of the results
only concerned one-particle systems on graphs. In this talk we introduce
models of interacting many-particle systems where we distinguish
between interactions that are localised on the vertices of the graph
and contact interactions that are present whenever two particles are
at the same position along any edge of the graph. Based on these
models which form a generalization of the well-known Lieb-Liniger
model, we are led to an investigation of the occurence or
non-occurence of Bose-Einstein condensation (BEC). We will, for
completeness, start with systems of non-interacting particles and
distinguish between graphs that show BEC and such that do not. We then
turn attention towards interacting systems and show that strong
repulsive contact interactions suppress the occurence of BEC.