We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limi...
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We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. Previously, the only result for the 3D energy critical case was Hong et al. (J Funct Anal 270(1):34-67, 2016), which proved the uniqueness part of the argument in the case of small solutions. In the main part of this paper, we develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false endpoint trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new hierarchical uniform frequency localization (HUFL) property for the GP hierarchy and use it to prove a new type of uniqueness theorem. The HUFL property reduces to a new statement even for NLS. With the help of Colliander et al. (Ann Math (2) 167(3):767-865, 2008) and Ionescu and Pausader (Duke Math J 161:1581-1612, 2012) which proved the global well-posedness for the quintic NLS, this new uniqueness theorem establishes global uniqueness.
Substituted polycyclic aromatic hydrocarbons (SPAHs) are being intensively investigated, considering their high toxicity. Additionally, the mechanism of the effect of substituents on the removal of SPAHs and the activ...
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We consider the cubic and quintic nonlinear Schrödinger equations (NLS) under the d and Td energy-supercritical setting. Via a newly developed unified scheme, we prove the unconditional uniqueness for solutions t...
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