Appears in collection : Nonlinear Waves Trimester - June Conference

We prove that Gibbs measures of nonlinear Schroedinger equations of Hartree-type arise as high-temperature limits of appropriately modified thermal states in many-body quantum mechanics. In dimensions d=2,3 these Gibbs measures are supported on singular distributions and Wick ordering of the interaction is necessary. Our proof is based on a perturbative expansion in the interaction, organised in a diagrammatic representation, and on Borel resummation of the resulting series