On the WellPosedness and Scattering for the GrossPitaevskii Hierarchy via Quantum de Finetti
Abstract
We prove the existence of scattering states for the defocusing cubic GrossPitaevskii (GP) hierarchy in . Moreover, we show that an exponential energy growth condition commonly used in the wellposedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 July 2014
 DOI:
 10.1007/s1100501406932
 arXiv:
 arXiv:1311.2136
 Bibcode:
 2014LMaPh.104..871C
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 35Q55;
 81V70
 EPrint:
 AMS Latex, 19 pages