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Article Dans Une Revue Probability and Mathematical Physics Année : 2023

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

Résumé

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 the ground state of the system exhibits the complete Bose--Einstein condensation, and that the condensate is the unique minimizer of the 3D energy-critical nonlinear Schr\"odinger functional where the nonlinear term is coupled with the scattering energy of the interaction potential.
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Dates et versions

hal-03388105 , version 1 (15-03-2024)

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Phan Thành Nam, Julien Ricaud, Arnaud Triay. The condensation of a trapped dilute Bose gas with three-body interactions. Probability and Mathematical Physics, 2023, 4 (1), pp.91-149. ⟨10.2140/pmp.2023.4.91⟩. ⟨hal-03388105⟩
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