混合凝聚方程解Hartree型方程的收敛速度
Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data
摘要：
我们考虑一个系统的$p$组件的玻色子，其中每个组成的$N_{1},N_{2},\dots,N_{p}$粒子，分别。玻色子是三维的，通过广义相互作用势相互作用，其中包括库仑相互作用。我们设定初始条件来描述混合物凝聚，即，因子化状态的张量积。我们证明了在平均场区域中的多体薛定谔演化与相应的Hartree方程系统的$p$ -粒子动力学之间的差异是$O(N^{-1})$，其中$N=\sum_{q=1}^{p}N_{q}$。
英文摘要：
We consider a system of $p$ components of bosons, each of which consists of $N_{1},N_{2},\dots,N_{p}$ particles, respectively. The bosons are in three dimensions with interactions via a generalized interaction potential which includes the Coulomb interaction. We set the initial condition to describe a mixture condensate, i.e., a tensor product of factorized states. We show that the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding $p$-particle dynamics due to a system of Hartree equation is $O(N^{-1})$ where $N=\sum_{q=1}^{p}N_{q}$.
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