摘要：本文开头会先介绍理论知识和研究方法，接下来叙述整个推导过程并分析得到的理论结果的物理意义。我们通过考虑所谓的旋转自旋自由度在光阱下释放的旋转凝聚物[1-5]，将物质波孤子的分析扩展到多分量情况。基于理论和实验结果，我们引入了一个新的可积分模型，描述了物质玻孤子的旋转冷凝物的动力学性质[6-9]。我们采用反向散射方法来精确地求解这个模型。因此，我们预测未发现的物理现象的发生，例如宏观自旋进动和自旋转换。该费米气体的动力学行为由多方近似下的推广的Gross-Pitaevskii方程(GGPE)来描述。本文组织如下：在绪论中谈到了这一主题的一些当前进展，在第一章，简要回顾了凝聚体的平均场理论、巴格寥夫理论、玻色爱因斯坦凝聚、G-P方程和哈密顿量相关理论知识。在第二章第一节中，我们用这些结果，考虑在q1D体系中的旋转凝聚体。然后，说明了用于旋转凝聚体的耦合非线性方程的可积分条件，其中导出了确切的孤子解。在第二章第二节，我们经过已知函数替换总结了我们的研究结果。

关键词：玻色爱因斯坦凝聚；Gross-Pitaevskii方程；超冷原子；孤子

Abstract：In the second chapter, we talk about some of the current developments in this subject, and analyze the physical meaning of the theoretical results obtained. We extend the analysis of the material soliton to the multi-component case by considering the so-called rotational spin degrees of freedom of the release aggregates released under the optical trap [1-5]. Based on the theoretical and experimental results, we introduce a new integrable model, which describes the dynamic properties of the rotating condensate of the material glass soliton [6-9]. We use the backscatter method to accurately solve this model. Thus, we predict the occurrence of undiscovered physical phenomena, such as macro spin precession and spin conversion. The kinetic behavior of the Fermi gas is described by the generalized Gross-Pitaevskii equation (GGPE). This article is organized as follows. In the first chapter, we briefly review the theory of the average field of agglomerates, the Bage theory, the Bose Einstein condensate, the GP equation and the Hamiltonian correlation. In the first chapter, we briefly talk about the current progress of this topic. Theoretical knowledge. In the second chapter, we use these results to consider the rotating agglomerates in the q1D system. Then, the integrable conditions for the coupled nonlinear equations for the rotating agglomerates are illustrated, in which the exact soliton solutions are derived. In the second chapter of Chapter 2, we have summarized the results of our study by a known function.

Keywords: Wave color Einstein condensate; Gross-Pitaevskii equation; super-cold atoms; soliton

目录

第一章绪论...1

1.1玻色爱因斯坦冷凝的G-P动力学..1

1.2G-P非线性动力学用于伪旋转聚合物 4

1.2.1伪旋转冷凝物4

1.3巴格寥夫理论 6

1.3.1平均场理论6

1.4哈密顿量7

1.5Gross-Pitaevskii方程8

1.5.1约束引起的共振...9

1.6哈密尔顿模型9

1.7本章主要工作10

第二章计算方法....12

2.1GP近似下的呼吸振子 12

2.2函数变换 15

结论 17

致谢 18

参考文献.19

第一章绪论

由于以下两个原因：（1）通过施加磁场和激光，大多数系统参数，例如形状，维度，缩合物的内部状态，甚至原子间相互作用的强度是可控的[11];（2）由于稀释，平均场理论解释实验相当好。特别地，GrossPitaevskii（GP）方程证明其作为冷凝动力学的基本方程的有效性。原子气体的玻色爱因斯坦凝聚(BEC)吸引了在极低的温度下的量子多体系统理论和实验兴趣[10]，GP方程是非线性光学中非线性薛定谔NLS）方程的对应物[12]。因此基于非线性分析的研究是可能的和重要的。