论文标题
谭的接触是理论的完整性和自我矛盾的指标
Tan's contact as an indicator of completeness and self-consistency of a theory
论文作者
论文摘要
众所周知，可以通过使用以下三种方法中的任何一个：通过动量分布的渐近行为来计算Tan的接触；由Tan的绝热扫描定理；或通过操作员产品扩展作为交互项的期望值。我们认为，如果描述唯一的接触相互作用的Bose（或Fermi）系统的理论是自我一致的，那么在所有三种情况下都应导致相同的结果。作为一个例子，我们考虑了基于MFT的方法，并确定在MFT的现有近似值中，Hartree -Fock -Bogoliubov（HFB）方法是最自我一致的。实际上，HFB能够描述有关TAN接触稀释的Bose气体的现有实验数据，但无法预测其在大气体参数$（γ> 0.015）$的预期行为。因此，对于即使在零温度下，也需要通过考虑第二个比第二个的波动来扩大近似值的适当描述，即使在零温度下，也需要扩大这种近似值。
It is well known that, Tan's contact could be calculated by using any of following three methods: by the asymptotic behavior of momentum distribution; by Tan's adiabatic sweep theorem; or by the operator product expansion as an expectation value of the interaction term. We argue that, if a theory describing Bose (or Fermi) system with the only contact interaction is self consistent, then it should lead to the same result in all three cases. As an example we considered MFT based approaches and established that among existing approximations of MFT, the Hartree - Fock - Bogoliubov (HFB) approach is the most self consistent. Actually, HFB is able to describe existing experimental data on Tan's contact for dilute Bose gas, but fails to predict its expected behavior at large gas parameter $(γ> 0.015)$. So, for appropriate description of properties of a Bose gas even at zero temperature, this approximation needs to be expanded by taking into account fluctuations in higher order then the second one.
