Using advanced stochastic methods (time-dependent quantum Monte Carlo, TDQMC) we explore the ground state of 1D and 2D artificial atoms with up to six bosons in harmonic trap where these interact by long-range and short-range Coulomb-like potentials (bosonic quantum dots). It is shown that the optimized value of the key variational parameter in TDQMC named nonlocal correlation length is close to the standard deviation of the Monte Carlo sample for one boson and it is slightly dependent on the range of the interaction potential. Also it is almost independent on the number of bosons for the 2D system thus confirming that the spatial quantum non-locality experienced by each particle is close to the spatial uncertainty exhibited by the rest of the particles. The intimate connection between spatial non-locality and quantum correlations is clearly evidenced.

中文翻译：

---

受限量子系统中的空间非定域性：与量子相关性的联系

我们使用先进的随机方法（时间相关量子蒙特卡罗，TDQMC）探索一维和二维人造原子的基态，在谐波陷阱中具有多达六个玻色子，其中它们通过长程和短程库仑样势（玻色子）相互作用量子点）。结果表明，TDQMC中称为非局部相关长度的关键变分参数的优化值接近于一个玻色子的蒙特卡罗样本的标准偏差，并且略微依赖于相互作用势的范围。此外，它几乎与 2D 系统的玻色子数量无关，因此证实了每个粒子所经历的空间量子非局域性接近于其余粒子所表现出的空间不确定性。