论文标题
通过相位场晶体模型探索Bose-Einstein凝结物中的分叉
Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models
论文作者
论文摘要
为了促进Bose-Einstein冷凝物（BEC）中模式形成和相关相变的分析，我们提出了从非局部格罗斯 - 彼得斯基（Bross-Pitaevskii）方程的明确近似映射，其立方非线性到相位场晶体（PFC）模型。该近似值靠近靠近超丝酚醇的相变边界。简化的PFC模型允许使用标准软件通过数值路径延续来探索分叉和相变。在揭示系统中存在分叉的详细结构的同时，我们证明了局部状态的存在。最后，我们讨论高阶非线性如何改变代表系统中发现的过渡的分叉图的结构。
To facilitate the analysis of pattern formation and of the related phase transitions in Bose-Einstein condensates (BECs) we present an explicit approximate mapping from the nonlocal Gross-Pitaevskii equation with cubic nonlinearity to a phase field crystal (PFC) model. This approximation is valid close to the superfluid-supersolid phase transition boundary. The simplified PFC model permits the exploration of bifurcations and phase transitions via numerical path continuation employing standard software. While revealing the detailed structure of the bifurcations present in the system, we demonstrate the existence of localized states. Finally, we discuss how higher-order nonlinearities change the structure of the bifurcation diagram representing the transitions found in the system.
