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

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 Added by Thomas Chen
 Publication date 2013
  fields Physics
and research's language is English




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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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We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in $R^3$. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdos, Schlein and Yau, cite{esy1,esy2,esy3,esy4}.
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