AI 中文总结
研究一维不完美人工晶体捕获的玻色气体中，空位对其基态能量等性质的影响。采用平均场近似和“离散归一化梯度流”方法求解方程，观察到基态能量变化、能隙及玻色子分布特点，还能获取化学势。
AI 中文摘要
对于由不完美一维人工晶体捕获的弱相互作用玻色气体，我们研究了其点缺陷即空位对系统基态性质的影响。在平均场近似框架下，使用“离散归一化梯度流”方法（即虚时方法）数值求解相应的格罗斯 - 皮塔耶夫斯基方程。晶体通过对玻色气体施加外部狄拉克梳状势人工产生，空位通过随机移除预定数量的δ函数创建。我们观察到，随着随机移除的δ函数数量增加，基态能量从完美晶体情况的值呈指数下降，直至达到玻色气体自由时的值。报告了不同玻色子相互作用强度和几种系统尺寸下的基态能量，并对只有一个空位的晶体外推到无穷大情况。还观察到完美系统和有空位系统的基态能量之间存在能隙，当δ强度\(P_0 = 10\)且粒子相互作用强度\(g \leq 0.1\)时更明显。此外，报告了晶体内的玻色子分布，其概率密度函数在空位周围显示出局域化特征，随着\(g\)增加而消失。从基态能量可立即得到化学势。
英文摘要
For a weakly interacting Bose gas trapped by an imperfect one-dimensional artificial crystal, we study the effect of its punctual defects, i.e. vacancies, on the ground state properties of the system. In the framework of the mean field approximation, we numerically solve the corresponding Gross-Pitaevskii equation using the ``Gradient Flow with Discrete Normalization'' method, also known as the imaginary time method. The crystal is artificially produced by applying an external Dirac comb potential to the Bose gas where vacancies are created by randomly removing a predetermined number of deltas. We observe that as the number of randomly removed deltas increases, the ground state energy decreases exponentially from its value for the perfect crystal case until it reaches its value when the Bose gas is free. The ground state energy is reported for different magnitudes of the interaction between bosons and several system sizes which we extrapolate to infinity for the crystal with only one vacancy. Also, we observe the presence of an energy gap between the ground state energies of the perfect system and that with a vacancy, which is more noticeable for values of the particle interaction magnitude $ g \leq 0.1$, when the delta strength $P_0 = 10$. In addition, we report the boson distributions within the crystal, %inside a box with periodic boundary conditions, i.e. the probability density functions which show localization features around vacancies which disappear as $g$ increases. From the ground state energy, the chemical potential is obtained immediately.
Comments8 pages, 8 figures
