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On the Well-Posedness and Scattering for the Gross–Pitaevskii Hierarchy via Quantum de Finetti

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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 exponential 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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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, USA

    Thomas Chen & Nataša Pavlović

  2. Fachbereich Mathematik, Universität Tübingen, Tübingen, Germany

    Christian Hainzl

  3. Institute of Science and Technology Austria (IST Austria), Klosterneuburg, Austria

    Robert Seiringer

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  1. Thomas Chen
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Correspondence to Thomas Chen.

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Chen, T., Hainzl, C., Pavlović, N. et al. On the Well-Posedness and Scattering for the Gross–Pitaevskii Hierarchy via Quantum de Finetti. Lett Math Phys 104, 871–891 (2014). https://doi.org/10.1007/s11005-014-0693-2

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