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

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.

AMS Latex, 19 pages

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• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Scattering for the non-radial 3D cubic nonlinear Schroedinger equation
• Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
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Cited by in corpus (11)

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• Local existence of solutions to Randomized Gross-Pitaevskii hierarchies
• Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
• Uniqueness of Solutions to the Spectral Hierarchy in Kinetic Wave Turbulence Theory
• Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}$
• On well-posedness and uniqueness for general hierarchy equations of Gross-Pitaevskii and Hartree type
• Mean field approximation of many-body quantum dynamics for Bosons in a discrete numerical model