Recent advances in Bose-Einstein condensation

Sohinger: We study interacting quantum Bose gases in thermal equilibrium on a lattice. In this framework, we establish convergence of the grand-canonical Gibbs states to their mean-field (classical field) and large-mass (classical particle) limit.
Our analysis is based on representations in terms of ensembles of interacting random loops, namely the Ginibre loop ensemble for quantum bose gases and the Symanzik loop ensemble for classical scalar field theories. For small enough interactions, we obtain corresponding results in the infinite volume limit by means of cluster expansions. This is joint work with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein.

Ueltschi:In 1953 Feynman suggested that Bose-Einstein condensation is related to the presence of long cycles in what is now known as the Feynman-Kac representation. Suto proved equivalence in the case of non-interacting systems (1993 and 2002). He recently proposed a proof for interacting systems. I will discuss a lattice model where Bose-Einstein condensation can be excluded, and yet infinite cycles are likely. This seems to bring a contradiction. I hope for constructive feedback from the audience, that could shed light on this question.