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arXiv 0803.1799quant-phnlin.CD
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具有吸引1/r相互作用的玻色-爱因斯坦凝聚体的动力学和稳定性

Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction

Holger Cartarius, Tomaž Fabčič, Jörg Main, Günter Wunner

备注：
Corrected the original usage of two inconsistent energy units in some equations and in Figs. 2, 4, 5, and 6; 12 pages 12 figures
发表信息：
Phys. Rev. A 78, 013615 (2008)
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摘要：

用变分法和数值精确计算方法研究了具有吸引1/r相互作用的玻色-爱因斯坦凝聚体的含时扩展Gross-Pitaevskii方程.我们发现，这些凝聚体表现出已知的签名从自治哈密顿系统的非线性动力学。在临界值的散射长度的切线分叉中创建的两个固定的解决方案被确定为椭圆和双曲不动点，对应于稳定和不稳定的定态的冷凝。稳定的定态被椭圆形的岛包围，对应于凝结物随时间周期性地振荡，而在不稳定区域中的凝结物波函数在有限时间内发生崩溃。对于负散射长度以下的切分叉没有固定的解决方案存在，即，冷凝物总是不稳定的并且会塌陷。

英文摘要：

The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dynamics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed points, corresponding to stable and unstable stationary states of the condensate. The stable stationary state is surrounded by elliptical islands, corresponding to condensates periodically oscillating in time, whereas condensate wave functions in the unstable region undergo a collapse within finite time. For negative scattering lengths below the tangent bifurcation no stationary solutions exist, i.e., the condensate is always unstable and collapses.

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