零温囚禁玻色子气体中对激发的可解模型
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相同的单粒子量子态。我们的目标是研究在被囚禁的稀原子气体中粒子激发到非单粒子宏观态的随时间变化的方面。我们采用这样的观点，即原子被成对激发，使得它们在时间t从单粒子态到矢量位置x和y的散射由成对激发函数K 0（x，y，t）描述。假设宏观态的波函数满足与时间无关的非线性薛定谔方程，求解了慢变外势下K 0的非定域方程.对于零初始激励（在t=0时K 0 =0）和足够大的t，我们在任意距离的单变量Lommel函数中渐近地计算K 0| X-Y|.
英文摘要：
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|.
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。
