超流体溃坝中的量子起伏涌潮、彩虹与事件视界
Quantum undular bores, rainbows, and event horizons in superfluid dam breaks
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中文总结 AI 辅助
本研究通过Gross-Pitaevskii方程研究BEC溃坝中的量子起伏涌潮，揭示其与双彩虹焦散结构的类比，并证明非微扰区域存在自感声学视界，为量子流体动力学提供新见解。
中文摘要 AI 辅助
从玻色-爱因斯坦凝聚体（BEC）中突然移除势垒会产生流体动力学溃坝的量子版本，并导致丰富的波动动力学，这与自旋系统中畴壁动力学等其他局域缺陷问题具有相似性。以$\Delta n$表示坝两侧上部$n_{1}$与下部$n_{0}$储库之间的初始密度差，我们使用Gross-Pitaevskii方程研究准一维情形，涵盖微扰（$\Delta n \ll n_{0}$）和非微扰（$\Delta n \sim n_{1}$）两种区域。在微扰区域中，形成一对向外传播的色散波包，可视为量子版本的起伏潮涌，其在长时间下具有以艾里函数积分表示的解析形式，波长随$(\hbar^2 t)^{1/3}$增长。艾里函数是修饰结构稳定折叠焦点的普适波函数，在焦点处成对光线会聚；确实，我们证明量子溃坝问题具有与自然发生的双彩虹焦散现象相同的射线结构，包括两弓之间无光散射的亚历山大暗带：我们将溃坝中的中间密度平台识别为类似的“静默带”，其中仅存在倏逝声波。在非微扰溃坝的相反区域中，我们证明当$\Delta n \geq (8/9)n_{1}$时会出现自感声学视界。文中还讨论了放大量子起伏的可行实验方案，以及另一种色散波产生方案，即在盒形陷阱中对BEC施加恒定流动。
英文摘要
The sudden removal of a potential barrier from a Bose-Einstein condensate (BEC) gives rise to a quantum version of a hydrodynamic dam break and leads to rich wave dynamics that have similarities to other localized defect problems such as domain wall dynamics in spin systems. Denoting $Δn$ as the initial difference in density between the upper $n_{1}$ and lower $n_{0}$ reservoirs on either side of the dam, we use the Gross-Pitaevskii equation to study the quasi-one dimensional case in both perturbative ($Δn \ll n_{0}$) and non-perturbative ($Δn \sim n_{1}$) regimes. In the perturbative regime a pair of outwardly propagating dispersive wavepackets forms which can be viewed as quantum versions of undular tidal bores that have analytic forms at long times in terms of the integrals of Airy functions with a wavelength that grows as $(\hbar^2 t)^{1/3}$. Airy functions are the universal wave functions that dress structurally stable fold caustics where pairs of rays coalesce, and, indeed, we show that the quantum dam break problem has the same ray structure as the naturally occurring caustic phenomenon of a double rainbow, including Alexander's dark band between the two bows where no light is scattered: we identify the intermediate density plateau in the dam break as an analogous `silent band' where only evanescent sound waves can exist. In the opposite regime of a non-perturbative dam break we show that a self-induced sonic horizon occurs when $Δn \geq (8/9)n_{1}$. A discussion of possible experimental schemes for amplification of quantum undulations is included as well as an alternative scheme for dispersive wave generation where a constant flow is imprinted on a BEC in box trap.
发表机构
- McMaster University（麦克马斯特大学）
- Kirchhoff-Institut für Physik, Universität Heidelberg（海德堡大学基尔霍夫物理研究所）
- Physikalisches Institut, Universität Heidelberg（海德堡大学物理研究所）
- University of Massachusetts Boston（马萨诸塞大学波士顿分校）
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