紧波导中无限强相互作用费米气体的精确解
Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
摘要：
本文给出了具有无限排斥力的准一维自旋1/2费米子基本系统在任意约束势下的精确解析解。本征函数的构造采用Girardeau的硬核接触边界条件和群论方法相结合的方法，保证了所得到的态同时是$S$和$S_z$的本征态，并满足奇排列下的反对称性。我们发现，总的基态密度分布的行为像极化的非相互作用费米子，而自旋相关的密度显示不同的自旋配置的不同属性。我们还讨论了大而有限排斥作用下的基态分裂。
英文摘要：
We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for arbitrary confining potential. The eigenfunctions are constructed by the combination of Gireardeau's hard-core contacting boundary condition and group theoretical method which guarantees the obtained states to be simultaneously the eigenstates of $S$ and $S_z$ and fulfill the antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.
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