超稀薄准二维玻色-玻色液体混合物
Ultradilute quasi-two-dimensional Bose-Bose liquid mixtures
AI总结：
研究超稀薄$^{39}$K玻色-玻色混合物和液滴，用QMC获状态方程，基于此开发二维QMC密度泛函。计算表明中等压缩时该泛函结果与三维泛函吻合且成本低，仅强限制系统接近二维LHY预测，二维LHY泛函适用范围窄。
AI中文摘要：
我们研究了超稀薄的$^{39}$K玻色-玻色体混合物和处于外部谐波势中的液滴，该势在一个空间方向上限制它们趋向二维（2D）极限。在$T = 0$时，使用包含$s$波散射长度$a$和有效范围$r_{\rm eff}$信息的相互作用势，通过量子蒙特卡罗（QMC）获得了几种限制条件下的状态方程。使用两种不同的相互作用势模型进行计算，确定了状态方程在$a$和$r_{\rm eff}$方面具有通用性的限制范围。基于QMC状态方程，我们为每个限制强度开发了一个二维QMC密度泛函，并将其与局部密度近似一起用于确定自束缚液滴的性质。对于中等压缩情况，使用二维QMC泛函获得的能量和液滴轮廓与使用三维泛函获得的结果吻合良好，同时显著降低了计算成本，并提供了一种在向二维过渡时的一致方法。值得注意的是，我们的结果仅在观察到$a$和$r_{\rm eff}$通用性的最强限制系统中接近二维平均场（MF）+李-黄-杨（LHY）预测。这意味着二维LHY泛函适用的限制范围非常窄，这对涡旋研究具有重要影响。
英文摘要：
We study ultradilute $^{39}$K Bose-Bose bulk mixtures and droplets in an external harmonic potential that confines them in one spatial direction towards the two-dimensional (2D) limit. Equations of state for several confinements are obtained with quantum Monte Carlo (QMC) at $T=0$, using interaction potentials that include information on the $s$-wave scattering length $a$ and the effective range $r_{\rm eff}$. Performing the calculations using two different interaction potential models we have determined the range of confinements for which equations of state are universal in terms of $a$ and $r_{\rm eff}$. Based on the QMC equation of state, we develop a 2D QMC density functional for each confinement strength and use it together with the local density approximation to determine properties of the self-bound drops. For moderate squeezing, energies and droplet profiles obtained using the 2D QMC functional agree well with those obtained using 3D functionals, while offering a substantial reduction in computational cost, and a consistent approach in crossover to 2D. Noticeably, our results approach 2D mean-field (MF) + Lee-Huang-Yang (LHY) predictions only for the most strongly confined systems for which universality in terms of $a$ and $r_{\rm eff}$ is observed. This implies a very narrow range of confinements for which 2D LHY functionals are applicable, which has important consequences for the study of vortices.
