论文标题
超越平均场：冷凝水和配对激发
Beyond mean field: condensate coupled with pair excitations
论文作者
论文摘要
我们证明了偏微分方程系统的存在结果，该系统描述了在固定环境中稀释（t = 0）bose气体的近似凝结物波函数和成对兴奋核，在存在诱捕潜力和排斥性成对原子相互作用的情况下。值得注意的是，该系统中的冷凝物的hartree型方程包含非趋化颗粒的贡献，并且对激发核满足非线性操作员方程。这里研究的方程式是受格里芬（Griffin）的工作的启发，他在有限温度冷凝物研究中得出了该系统。所采用的技术包括一个变异原理，该原理利用了对兴奋性内核的单一Bogoliubov旋转与非线性操作员方程之间的连接。还包括用于构建解决方案的迭代程序。
We prove existence results for a system of partial differential equations describing the approximate condensate wavefunction and pair-excitation kernel of a dilute (T=0) Bose gas in the stationary setting, in the presence of a trapping potential and repulsive pairwise atomic interactions. Notably, the Hartree-type equation for the condensate in this system contains contributions from non-condensate particles, and the pair excitation kernel satisfies a nonlinear operator equation. The equations studied here are inspired by the work of Griffin, who derived this system in the study of finite temperature condensates. The techniques employed include a variational principle, which exploits the connection between unitary Bogoliubov rotations and a nonlinear operator equation for the pair excitation kernel. An iterative procedure for constructing solutions is also included.
