Derivation of the 3D quintic Gross--Pitaevskii equation

We study the time evolution of Bose–Einstein condensates with three-body interactions in the Gross–Pitaevskii regime. We show that Bose–Einstein condensation is preserved under many-body evolution and that the condensate wavefunction evolves according to the quintic Gross–Pitaevskii equation in $\mathbb{R}^3$, which is energy critical. In particular, we show that the effective coupling constant is universal and depends only on a three-body scattering hypervolume.

💡 Research Summary

The paper addresses the rigorous derivation of the three‑dimensional quintic Gross–Pitaevskii (GP) equation from the many‑body Schrödinger dynamics of a Bose gas with three‑body interactions in the Gross–Pitaevskii scaling regime. The authors consider a system of (N) identical bosons in (\mathbb R^{3}) described by the symmetric Hilbert space (\mathcal H_{N}=L^{2}_{\rm sym}(\mathbb R^{3N})) and the Hamiltonian
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