Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions
Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions
复制标题
玻色-爱因斯坦凝聚中的暗孤子振荡与多体相互作用
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
M. Salerno
中科院分区：
文献类型：
--
作者：
A. Kamchatnov;M. Salerno
考虑了在满足玻色-爱因斯坦凝聚体调制稳定性条件的情况下，暗物质波孤子通过由具有广义非线性的平均场Gross-Pitaevskii方程描述的非均匀雪茄形玻色-爱因斯坦凝聚体的动力学行为.深暗孤子的振荡频率的解析表达式推导出的非线性是任意函数的密度，而具体的结果进行了讨论的物理相关的情况下的一个五阶非线性建模两个和三体相互作用，分别。与通常的（立方）Gross-Pitaevskii方程相反，已知暗孤子有效质量为常数（等于2），在存在三阶-五阶非线性的情况下，我们发现有效质量取决于初始密度背景与五阶和三阶非线性系数之比的乘积，这导致直接从暗孤子动力学测量三体相互作用的有趣的可能性。对五阶Gross-Pitaevskii方程的解析解和直接数值模拟结果的比较表明，两者吻合较好，从而证实了本文方法的有效性.
We consider the dynamics of dark matter wave solitons moving through non-uniform cigar-shaped Bose–Einstein condensates described by the mean field Gross–Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose–Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic–quintic nonlinearity modelling two- and three-body interactions, respectively. Opposite to the usual (cubic) Gross–Pitaevskii equation for which the dark soliton effective mass is known to be constant (equal to 2), in the presence of a cubic–quintic nonlinearity we find that the effective mass depends on the product of the initial density background and the ratio between the coefficient of quintic and cubic nonlinearities, this leading to the interesting possibility of measuring three-body interactions directly from the dark soliton dynamics. A comparison between analytical results and direct numerical simulations of the cubic–quintic Gross–Pitaevskii equation shows good agreement between them which confirms the validity of our approach.