二维量子液滴的变分近似
The variational approximation for two-dimensional quantum droplets
摘要：
研究了二维玻色-爱因斯坦凝聚体在量子涨落作用下的动力学行为。用变分法分析了局域密度分布量子液滴的性质。结果表明，超高斯函数给出了一个很好的近似的基本量子点和液滴与非零涡的轮廓。得到了量子点参数的动力学方程。这些方程的不动点决定了量子点的参数。估计了量子点在定态附近的小振荡周期。结果表明，量子涨落强度的周期性调制可以驱动不同的过程，包括量子点参数的共振振荡，波的发射和量子点分裂成更小的液滴。
英文摘要：
The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum fluctuations is studied. The properties of localized density distributions, quantum droplets (QDs), are analyzed by means of the variational approach. It is demonstrated that the super-Gaussian function gives a good approximation for profiles of fundamental QDs and droplets with non-zero vorticity. The dynamical equations for parameters of QDs are obtained. Fixed points of these equations determine the parameters of stationary QDs. The period of small oscillations of QDs near the stationary state is estimated. It is obtained that periodic modulations of the strength of quantum fluctuations can actuate different processes, including resonance oscillations of the QD parameters, an emission of waves and a splitting of QDs into smaller droplets.
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