论文标题
与单数三体相互作用的弱相互作用的玻色子的收敛速率
Rate of convergence towards mean-field evolution for weakly interacting bosons with singular three-body interactions
论文作者
论文摘要
在本文中，我们研究了$ n $弱相互作用的玻色子系统的动力学，并在三个维度上具有奇异的三体相互作用。通过假设对初始数据$ψ_{n，0} =φ_{0}^{\ otimes n} $和三重碰撞，我们证明，在许多粒子极限中，其平均场近似收敛到Quintic Hartree动力学。此外，我们证明，与$ o（n^{ - （1+4a）/（3+2a）/（3+2a）}）的收敛速率对于$ o（n^{ - （1+4a）/（3+2a）}）$对于$φ_{0} \ in H^{（3/2） $ o（n^{ - 1}）$ for $ a> 1 $。我们的证明是基于并扩展了Fock空间方法的。
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 $Ψ_{N,0}=φ_{0}^{\otimes N}$ 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 $φ_{0}\in H^{(3/2)+a}(\mathbb{R}^{3})$ where $0\leq a<1/2$ and $O(N^{-1})$ for $a>1$. Our proof is based on and extends the Fock space approach.
