一维极化BEC中的孤立波及其稳定性论文设计

一维极化 BEC 中的孤立波及其稳定性摘要：波色爱因斯坦凝聚在当今物理学界备受人们关注的热门研究领域之一，它是一种崭新奇特的物质状态，随着科技的发展，激光冷却技术等的发展，实验上 BEC 实现以来，人们已经对 BEC 的动力学稳定性，热力学稳定性等方面进行了研究并且取得了一定的成果。孤立波是一种可以稳定传播的物质形态，波色爱因斯坦凝聚中研究孤立波是当今非线性研究领域的一个热点。在本文研究了一维偶极 BEC 中的孤立波及其稳定性，内容如下：首先，理论上介绍了 BEC 的提出，BEC 的发展以及 BEC 的实验研究等，并对孤立波的发现做了的说明和解释;然后，详细介绍了 G-P 方程，推导了考虑外势的 G-P 方程，并将 G-P 方程进行无量纲化；其次，对考虑了偶极相互作用的准一维周期势中的孤立波进行了理论模型和数值结果的研究，接着，采用线性稳定分析，对孤立波的稳定性进行了分析和研究；最后是对全文的总结。关键词：波色-爱因斯坦凝聚 G-P 方程 孤立波 稳定性分析Abstract: Bose-Einstein condensation is one of the hot research topics in physics today. It is a new and peculiar state of matter. With the development of science and technology, the development of laser cooling technology, etc. The dynamic stability and thermodynamic stability of BEC have been studied and some results have been achieved. Solitary waves are a form of matter that can propagate steadily.This article studies the solitary waves and their stability in the one-dimensional dipole BEC. First, the theory is introduced, the development of BEC, the experimental research of BEC, etc., and the solitary waves are explained and explained; then, The GP equation is introduced in detail, and the GP equation is dimensionless. Secondly, the theoretical model and numerical results are studied on the solitary waves in the one-dimensional periodic potential. Finally, the stability of the solitary waves is analyzed by linear stability analysis. Conducted analysis and research.Keywords: Bose-Einstein cond...