标题： 激发态在托马斯-费米极限中：一种变分方法 显示英文标题

标题： Excited states in the Thomas-Fermi limit: a variational approach

摘要： 玻色-爱因斯坦凝聚体的激发态在具有排斥原子相互作用和简谐势的格罗斯-皮塔耶夫斯基方程的半经典（托马斯-费米）极限下被考虑。 利用平均拉格朗日方法，对局部凝聚体上的暗孤子（密度凹陷）相对于简谐势和其他暗孤子的相对动力学进行近似。 这使得能够根据化学势参数完全表征暗孤子的平衡位置。 它还提供了对暗孤子在这些平衡点附近振荡频率的解析把握。 渐近预测被推广到任意数量的暗孤子，并通过2-孤子和3-孤子配置的数值计算得到验证。 显示英文摘要

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.