格罗斯-皮塔耶夫斯基方程
偶极子
期限(时间)
俘获
动力学(音乐)
谐波
玻色-爱因斯坦凝聚体
谐波电位
理论(学习稳定性)
统计物理学
非线性系统
物理
经典力学
量子力学
计算机科学
机器学习
生态学
生物
声学
作者
Brahim Alouini,Hichem Hajaiej
标识
DOI:10.1142/s0219530522500117
摘要
The purpose of this paper is to study the dynamics of solutions to an extended Gross–Pitaevskii equation that models the formation of droplets in a dipolar Bose–Einstein condensate (BEC). The formation of these droplets has been recently discovered by driving the BEC into the strongly dipolar regime. Surprisingly, instead of collapsing, the system formed stable droplets. So far, no rigorous mathematical explanation has been proved. To the best of our knowledge, only experimental results have been obtained. The goal of this paper is to validate this breakthrough discovery. Many predictions/ conjectures properties of these droplets have been stated by some research groups in physics and engineering. In particular, it has been claimed that the stability of these droplets is a consequence of the presence of the damping term in the extended Gross–Pitaevskii equation under study. This term describes the three-body loss process. To accurately model the dynamics of formation of these droplets, it is necessary to consider a time-dependent harmonic trapping potential as well as other terms with different types of nonlinearity among them that describe the Lee–Huang–Yang (LHY). This presents some challenges that will be solved in this paper.
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