论文标题
通过一个光原子在一个维度上结合重费
Binding of heavy fermions by a single light atom in one dimension
论文作者
论文摘要
我们考虑$ n $相同的费米子通过零范围的吸引力相互作用的问题，在一个维度上具有较轻的原子。使用基于Skorniakov和Ter-Martirosian方程的少数身体方法，我们确定了四聚体，Pentamer和Hexamer出现的能量和临界质量比。对于大$ n $，我们通过基于托马斯 - 弗米近似的平均场理论分析解决问题。当重型质量比超过临界值时，该系统就会绑定，该临界值在$ n $时增长为$ n^3 $。我们还采用了一种更复杂的Hartree-fock方法，事实证明，该方法与Thomas-Fermi近似相当于确定能量，但可以更好地描述簇的显微镜结构。
We consider the problem of $N$ identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the energies and the critical mass ratios for the emergence of the tetramer, pentamer, and hexamer. For large $N$, we solve the problem analytically by using the mean-field theory based on the Thomas-Fermi approximation. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value which grows as $N^3$ at large $N$. We also employ a more sophisticated Hartree-Fock approach, which turns out to be equivalent to the Thomas-Fermi approximation for determining the energies, but provides a better description of the microscopic structure of the clusters.
