标题： 零温下束缚玻色气体中对激发的可解模型 显示英文标题

标题： Solvable model for pair excitation in trapped Boson gas at zero temperature

摘要： 在玻色-爱因斯坦凝聚中，宏观上大量的粒子占据同一个单粒子量子态。 我们的目标是研究被束缚的稀疏原子气体中，粒子激发到不同于单粒子宏观态的状态的时间依赖特性。 我们认为原子是以对的形式被激发的，因此它们从单粒子态散射到时间t时的矢量位置x和y由双激发函数K0(x,y,t)描述。 我们在假设宏观态的波函数满足时间独立的非线性薛定谔方程的前提下，求解在缓慢变化的外部势下K0的非局部方程。 对于初始激发为零（t=0时K0=0）且足够大的t，我们根据任意距离|x-y|的单变量洛梅尔函数渐近地评估K0。 显示英文摘要

摘要： In Bose-Einstein condensation, a macroscopically large number of particles occupy the same single-particle quantum state. Our goal is to study time-dependent aspects of particle excitations to states other than the single-particle macroscopic state in trapped dilute atomic gases. We adopt the view that atoms are excited in pairs so that their scattering from the single-particle state to vector positions x and y at time t is described by the pair-excitation function, K0(x,y,t). We solve a nonlocal equation for K0 under a slowly varying external potential by assuming that the wave function of the macroscopic state satisfies a time-independent nonlinear Schroedinger equation. For zero initial excitation (K0=0 at t=0) and sufficiently large t, we evaluate asymptotically K0 in terms of the one-variable Lommel function for any distance |x-y|.