论文标题
控制“智能”瞬态陷阱变化中的非自主物质波
Controlling nonautonomous matter waves in "smart" transient trap variations
论文作者
论文摘要
在本文中，我们研究了在雪茄形的玻色 - 因斯坦冷凝物的背景下，在不同的“智能”瞬态陷阱变化中非自治物质波的可控行为。通过利用自动相似性转换，我们将非自主的GROSS-PITAEVSKII（GP）方程式降低为椭圆形方程，该方程允许孤子解决方案。此过程导致一个一致性方程，该方程的形式是Riccati方程的形式。通过Cole-Hopf转换，Riccati和线性Schrödinger方程之间的连接在这里被利用，以引入时间陷阱变化。在我们的研究中，我们探讨了使用一个维度可解决（ES）势及其新建造的有理扩展的可能性，作为引入有趣的时间陷阱调制的时间功能。常规电位及其合理扩展在结构上不同的事实导致了不同的时间调制。据表明，在这两种情况下，孤子行为相对于压缩的行为都大不相同。
In this paper, we study the controllable behavior of nonautonomous matter waves in different "smart" transient trap variations in the context of the cigar-shaped Bose-Einstein condensates. By utilizing a self-similarity transformation we reduce the nonautonomous Gross-Pitaevskii (GP) equation to the elliptic equation that admits soliton solutions. This procedure leads to a consistency equation which is in the form of Riccati equation. The connection between the Riccati and the linear Schrödinger equation, through the Cole-Hopf transformation, is exploited profitably here to introduce temporal trap variations. For our study, we explore the possibility of using one dimensional exactly solvable (ES) potentials and their newly constructed rational extensions, as functions of time to introduce interesting temporal trap modulations. The fact that the regular potentials and their rational extensions being structurally different, leads to different temporal modulations. It is exhibited that the soliton behavior with respect to compression in both these cases is quite different.
