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arXiv · 2110.08195

The condensation of a trapped dilute Bose gas with three-body interactions

Phan Thành Nam·Julien Ricaud·Arnaud Triay
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Abstract

We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the system is a convex superposition of minimizers of a 3D energy-critical nonlinear Schr\"odinger functional where the nonlinear coupling constant is proportional to the scattering energy of the interaction potential. In particular, the $N$-body ground state exhibits complete Bose--Einstein condensation if the nonlinear Schr\"odinger minimizer is unique up to a complex phase.

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Phan Thành Nam, Julien Ricaud, Arnaud Triay. 2021-10-15. The condensation of a trapped dilute Bose gas with three-body interactions. https://doi.org/10.2140/pmp.2023.4.91

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