论文标题
Lee-huang-yang效应抑制吸引力领域中的准二维量子崩溃
Suppression of the quasi-two-dimensional quantum collapse in the attraction field by the Lee-Huang-Yang effect
论文作者
论文摘要
在三个维度和二维（3D和2D）中量子崩溃是由吸引人的电位〜-1/r^2引起的。事实证明，在3D骨气气体中的平均场（MF）立方体自我抑制会抑制崩溃并造成缺失的基态（GS）。但是，立方非线性不足以抑制2D崩溃。我们证明，由MF状态周围的量子波动引起的Lee-hung-yang（Lhy）四分之一术语足以稳定2D气体对塌陷的稳定。通过包括LHY期限（LHY项）以及分析方法的数值解决方案，例如在与中心和Thomas-Fermi近似较小的较小距离处的波动函数的扩展，我们构建稳定的GS，以单次密度，〜1/R^{4/3}，但我们构建了稳定的GS。违反直觉，即使外部电势令人反感，稳定的GS也存在，强度降至一定的临界价值。给出了这一发现的解释。与GS一起，也产生了奇异的涡流状态，并通过分析发现其稳定性边界。不稳定的涡流自发转化为稳定的GS，将涡度驱逐到外围。
Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive potential ~ -1/r^2. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D bosonic gas suppresses the collapse and creates the missing ground state (GS). However, the cubic nonlinearity is not strong enough to suppress the 2D collapse. We demonstrate that the Lee-Hung-Yang (LHY) quartic term, induced by quantum fluctuations around the MF state, is sufficient for the stabilization of the 2D gas against the collapse. By means of numerical solution of the Gross-Pitaevskii equation including the LHY term, as well as with the help of analytical methods, such as expansions of the wave function at small and large distances from the center and the Thomas-Fermi approximation, we construct stable GS, with a singular density, ~ 1/r^{4/3}, but convergent integral norm. Counter-intuitively, the stable GS exists even if the external potential is repulsive, with the strength falling below a certain critical value. An explanation to this finding is given. Along with the GS, singular vortex states are produced too, and their stability boundary is found analytically. Unstable vortices spontaneously transform into the stable GS, expelling the vorticity to periphery.
