光晶格中的量子液滴的变分动力学分析
Analysis of Variational Dynamics of Quantum Droplets in Optical Lattices
DOI: 10.12677/app.2024.145035, PDF,   
作者: 田 尚：浙江师范大学物理与电子信息工程学院，浙江 金华
关键词: 玻色–爱因斯坦凝聚；量子液滴；光晶格；拉格朗日变分法；Bose-Einstein； Quantum Droplet； Optical Lattice； Lagrange Variational Method
摘要: 本文研究了光晶格中量子液滴的波包动力学以及动力学不稳定性。我们从光晶格中量子液滴的Gross-Pitaevskii方程出发，通过紧束缚近似得到对应的离散方程，随后通过拉格朗日变分法对量子液滴进行动力学分析，并且通过元激发谱对量子液滴进行动力学不稳定性分析。结果表明，随着量子液滴相互作用强度的增强，波包的自束缚区域逐渐缩小，扩散区域逐渐增大，并且当液滴相互作用强度达到某一临界值时，原本存在的稳定振荡区域完全消失。通过光晶格中量子液滴的元激发谱可以发现，液滴相互作用强度发生微小的变化动力学不稳定性会发生显著变化，并且随着液滴相互作用强度的减小，动力学不稳定性区域逐渐收缩至准动量较小的区域。
Abstract: This article investigates the wave packet dynamics and dynamic instability of quantum droplets in optical lattices. Starting from the Gross-Pitaevskii equation for quantum droplets in optical lattices, we obtain the corresponding discrete equations through the tight-binding approximation. Subsequently, the dynamics of quantum droplets are analyzed using the Lagrangian variational method, and the dynamic instability is analyzed through the elementary excitation spectrum. The results indicate that as the interaction strength of quantum droplets increases, the self-trapped region of the wave packet gradually shrinks, while the diffusive region gradually expands. Furthermore, when the interaction strength of the droplets reaches a certain critical value, the originally stable oscillation region completely disappears. Through the elementary excitation spectrum of quantum droplets in optical lattices, it can be observed that minor changes in the interaction strength of the droplets lead to significant changes in dynamic instability. Additionally, as the interaction strength of the droplets decreases, the region of dynamic instability gradually contracts to areas with smaller quasi-momentum.
文章引用：田尚. 光晶格中的量子液滴的变分动力学分析[J]. 应用物理, 2024, 14(5): 301-308. https://doi.org/10.12677/app.2024.145035

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