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arXiv · 1311.2136

On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti

Thomas Chen·Christian Hainzl·Natasa Pavlovic·Robert Seiringer
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Abstract

We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ${\mathbb R}^3$. Moreover, we show that an energy growth condition commonly used in the well-posedness 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.

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Thomas Chen, Christian Hainzl, Natasa Pavlovic, Robert Seiringer. 2014-03-27. On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. https://doi.org/10.1007/s11005-014-0693-2

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