相互作用玻色子的对激发和平均场近似
Pair excitations and the mean field approximation of interacting Bosons, I
摘要：
在我们以前的工作\cite{GMM1}，\cite{GMM2}中，我们对相互作用玻色子的平均场近似作了修正.这种修正描述了离开凝聚体的粒子对的演化，并随后在凝聚体形成的背景上演化。在\cite{GMM2}中，我们假设相互作用与粒子数$N$无关来进行分析。这里我们考虑更强相互作用的情况。我们提供了一个新的透明的推导对激发的演变。事实上，我们得到一对线性方程描述他们的发展。此外，我们获得了独立于粒子数的先验估计，并使用这些来比较精确的近似动力学。
英文摘要：
In our previous work \cite{GMM1},\cite{GMM2} we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve on a background formed by the condensate. In \cite{GMM2} we carried out the analysis assuming that the interactions are independent of the number of particles $N$. Here we consider the case of stronger interactions. We offer a new transparent derivation for the evolution of pair excitations. Indeed, we obtain a pair of linear equations describing their evolution. Furthermore, we obtain apriory estimates independent of the number of particles and use these to compare the exact with the approximate dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
