Rate of convergence towards mean-field evolution for weakly interacting bosons with singular three-body interactions

Abstract

In this paper, we investigate the dynamics of a system of $N$ weakly interacting bosons with singular three-body interactions in three dimensions. By assuming factorized initial data ${\Psi }_{N,0}={\phi }_0^{\otimes N}$ and triple collisions, we prove that in the many-particle limit, its mean-field approximation converges to quintic Hartree dynamics. Moreover, we prove that the rate of convergence towards the mean-field quintic Hartree evolution is of $O(N^{-(1+4a)/(3+2a)})$ for ${\phi }_0\in H^{(3/2)+a}({\mathbb{R}}^3)$ where $0\le a<1/2$ and $O(N^{-1})$ for $a>1$. Our proof is based on and extends the Fock space approach.

arXiv commentarXiv admin note: text overlap with arXiv:1708.07278

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Cited by in corpus (2)

• The condensation of a trapped dilute Bose gas with three-body interactions
• Ground state energy of the low density Bose gas with three-body interactions