论文标题
具有接触相互作用的一维玻璃和费米气体的现场理论方面
Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
论文作者
论文摘要
我们研究了具有接触相互作用的一维（1D）玻色和费米气体的局部量子场理论，它们通过Girardeau的Bose-Fermi映射密切相互连接。虽然玻色子的拉格朗日人仅包括两体相互作用，但发现对费米子是必需的三体相互作用项。由于这种三体耦合，表征局部三合会相关性的三体触点出现在费米子的能量关系中，这是动量分布的总和之一。此外，我们在这两个系统中都应用了操作员产品的扩展，以得出动态结构因子和单粒子光谱密度的大能量和动量渐近分数。这些行为是普遍的，因为它们在任何温度下的任何一维散射长度都保持着。还讨论了在存在三体景点的情况下，tonks-girardeau气体的渐近造物是一种具有硬核排斥的玻色气体以及玻色弗米的通信。
We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.
