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

Abstract

We consider a trapped dilute gas of $N$ bosons in ${\mathbb{R}}^3$ interacting via a three-body interaction potential of the form $NV(N^{1/2}(x-y,x-z))$. 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 Schrödinger 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 Schrödinger minimizer is unique up to a complex phase.

arXiv comment57 pages

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• Dilute Bose gas with three-body interaction: recent results and open questions
• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond
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• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
• Homogeneous attractive Bose-Einstein condensates with repulsive three-body interactions: the two-dimensional case
• Validity of the Fröhlich model for a mobile impurity in a Bose-Einstein condensate