论文标题
$ \ mathbb {t}^{2} $ focus forcipic nls的严格推导
The rigorous derivation of the $\mathbb{T}^{2}$ focusing cubic NLS from 3D
论文作者
论文摘要
我们严格地将2D定期聚焦的立方NLS得出作为3D聚焦量子多体动力学的平均场限制，该量子多体动力学描述了具有$ x $方向的周期性边界条件的稀释式玻璃气体，并且在$ z $ - $ - 方向上的无限深度孔。这些系统的物理实验很少。我们发现，要满足在实验中观察NLS动力学的经验要求，即动能主导势能，有必要对系统参数施加额外的限制。这种限制使一个异常的耦合常数增加。
We derive rigorously the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics describing a dilute Bose gas with periodic boundary condition in the $x$-direction and a well of infinite-depth in the $z$-direction. Physical experiments for these systems are scarce. We find that, to fulfill the empirical requirement for observing NLS dynamics in experiments, namely, the kinetic energy dominates the potential energy, it is necessary to impose an extra restriction on the system parameters. This restriction gives rises to an unusual coupling constant.
