论文标题
在交替的捕获势能中保持的模式的稳定限制
Stability limits for modes held in alternating trapping-expulsive potentials
论文作者
论文摘要
我们阐述了一种陷阱超级管理（TEM）的方案，以二次潜在的形式定期切换和驱逐之间，作为稳定二维动力状态的手段，这是在临界崩溃的背景下由与强度g的立方体自动抗击所驱动的临界崩溃的背景。可以分别通过光学或BEC分别实施TEM方案，作为空间或时间周期性调制。考虑因素是通过数值模拟和变异近似（VA）进行的。在VA方面，动力学等于非线性Ermakov方程，而该方程又与线性Mathieu方程式相关。稳定边界被发现是G的函数和捕获电位的周期性调制的参数。在通常的崩溃阈值之下，以数值形式为g <5.85（在标准符号中）已知，稳定性受参数共振的开始受到限制。 VA准确预测了该稳定性极限，包括具有立方项的自我抑制符号（G <0）的设置。在G> 5.85时，在完整的数值模拟的帮助下发现了塌陷阈值。 G高于5.85的临界值的相对增加为〜1.5％，即使其大小很小，这是一个有意义的结果，因为倒塌阈值是通用常数，很难更改。
We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the backdrop of the critical collapse driven by the cubic self-attraction with strength g. The TEM scheme may be implemented, as spatially or temporally periodic modulations, in optics or BEC, respectively. The consideration is carried out by dint of numerical simulations and variational approximation (VA). In terms of the VA, the dynamics amounts to a nonlinear Ermakov equation, which, in turn, is tantamount to a linear Mathieu equation. Stability boundaries are found as functions of g and parameters of the periodic modulation of the trapping potential. Below the usual collapse threshold, which is known, in the numerical form, as g < 5.85 (in the standard notation), the stability is limited by the onset of the parametric resonance. This stability limit, including the setup with the self-repulsive sign of the cubic term (g < 0), is accurately predicted by the VA. At g > 5.85, the collapse threshold is found with the help of full numerical simulations. The relative increase of the critical value of g above 5.85 is ~ 1.5%, which is a meaningful result, even if its size is small, because the collapse threshold is a universal constant, which is difficult to change.
