论文标题
一个被困的利比尼格的单粒子密度矩阵
One-particle density matrix of a trapped Lieb-Liniger anyonic gas
论文作者
论文摘要
我们提供了一个零温度的一个粒子密度矩阵的彻底表征，在一个维度上相互作用的任何一个气体，从而利用了空间不均匀量子系统的现场理论描述的最新进展。我们首先通过与点相互作用重新访问同质的均质气体。在有限相互作用强度的单粒子密度基质的谐波Luttinger液体膨胀中，尚不清楚非普遍场振幅。我们从伯特阿萨茨公式中提取它们的田间形式，从而提供了这种相关函数的确切渐近扩展，从而将可用的结果扩展到了Tonks-Girardeau限制中。接下来，我们分析具有非平凡密度曲线的捕获气体。通过将最新的分析和数值技术应用于不均匀的Luttinger液体，我们为单粒子密度矩阵提供了精确的膨胀。我们为不同的限制电势介绍了我们的结果，突出了有关骨气气体的主要差异。
We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks-Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids,we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases.
