Abstract or Additional Information
The Hartree hierarchy is an infinite system of coupled PDEs which arises as an effective equation in the study of many-body quantum mechanics in the large particle limit. In this talk we will give an overview of this model (and the closely related Gross-Pitaevskii hierarchy), and discuss criteria which ensure that certain solutions of the hierarchy when equipped with focusing interactions must blow-up in finite time. We obtain results both with and without an assumption of finite variance on the initial data. The key tools involved are virial identities for the Hartree hierarchy, together with localized variants of these identities. The most delicate case of the analysis is the proof in the infinite variance case -- here, we use a suitable quantum de Finetti theorem and a carefully chosen truncation lemma allowing for the control of additional terms appearing from the localization procedure.