论文标题
半无限的一维玻色气和杂质状态的密度曲线
Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity
论文作者
论文摘要
我们研究边界对一个维度弱相互作用玻色子系统的影响。它强烈影响在边界位置完全抑制的玻色子密度。远离它，密度在平均场水平的愈合长度的距离上耗尽。量子波动大大修改了密度曲线。局部密度接近平均值作为距边界距离的逆平方。我们计算了与边界分离的任意分离时密度谱的分析表达式。然后，我们考虑在不均匀玻色子密度产生的电势中局部定位的问题。在平均场水平上，我们找到了结合状态的能量谱，相应波函数以及相互作用诱导的定位条件的确切结果。对玻色子密度的量子贡献产生了对结合状态能级的小校正。但是，这对于杂质与边界之间的远距离卡西米尔样相互作用至关重要。
We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.
