引力作用下旋转玻色爱因斯坦凝聚的基态
Ground State of Rotating Bose Einstein Condensates under Attractive Force
DOI: 10.12677/PM.2022.124069, PDF,   
作者: 张 萌：上海理工大学，理学院，上海
关键词: GP方程；Bose-Einstein凝聚；吸引力；GP Equation； Bose-Einstein Condensates； Attractive Force
摘要: 本文主要讨论二维吸引力作用下带有旋转速度的玻色爱因斯坦凝聚的基态。我们主要利用极大极小方法、Gagliardo-Nirenberg不等式、反磁不等式研究了Gross-Pitaevskii方程在限定条件下基态解的存在性情况。得到了当方程的基态解是存在的，当时，方程的基态解是不存在的。
Abstract: This paper mainly discusses the ground state of Bose-Einstein condensate with rotational velocity under the action of two-dimensional attraction. We mainly use the minimax method, Gagliardo-Nirenberg inequality and diamagnetic inequality to study the existence of the ground state solution of the Gross-Pitaevskii equation under limited conditions. It is obtained that the ground state solution of the equation exists when , and the ground state solution of the equation does not exist when .
文章引用：张萌. 引力作用下旋转玻色爱因斯坦凝聚的基态[J]. 理论数学, 2022, 12(4): 610-615. https://doi.org/10.12677/PM.2022.124069

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