变分法研究量子力学中的激发态
Excited states in the Thomas-Fermi limit: a variational approach
摘要：
在半经典极限下，考虑了具有原子间排斥相互作用和谐振势的Gros-Pitaevskii方程，研究了玻色-爱因斯坦凝聚体的激发态.利用平均拉格朗日方法近似计算了暗孤子（局域凝聚体上的密度骤降）相对于谐波势和相互之间的相对动力学。这允许一个完整的表征的暗孤子的平衡位置作为化学势参数的函数。它也产生了一个分析处理的暗孤子的振荡频率在这样的平衡。的渐近预测推广为任意数量的暗孤子，并证实了2-和3-孤子配置的数值计算。
英文摘要：
Excited states of Bose--Einstein condensates are considered in the semi-classical (Thomas-Fermi) limit of the Gross--Pitaevskii equation with repulsive inter-atomic interactions and a harmonic potential. The relative dynamics of dark solitons (density dips on the localized condensate) with respect to the harmonic potential and to each other is approximated using the averaged Lagrangian method. This permits a complete characterization of the equilibrium positions of the dark solitons as a function of the chemical potential parameter. It also yields an analytical handle on the oscillation frequencies of dark solitons around such equilibria. The asymptotic predictions are generalized for an arbitrary number of dark solitons and are corroborated by numerical computations for 2- and 3-soliton configurations.
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。
