从一维光晶格中释放的任意子噪声关联函数研究
Noise correlations in the expansion of one-dimensional anyon gases from a regular array

首先求解具有delta函数型相互作用的任意子气体的含时薛定谔方程，给出了其多体波函数的解析解，并在此基础上详细分析了相互作用情形和有相互作用情形下任意子噪声关联函数的特性。对于有相互作用的任意子气体，其噪声关联呈现出与相互作用情形下不同的特性：散射相位具有一定的空间分布，一系列线性而不是尖峰出现在噪声关联函数中；线性的宽度、取向以及位置与任意子的统计参数和粒子间相互作用强度的关系都非常密切。特别地，在TG极限下，也就是相互作用趋于限大的情形下，任意子的噪声关联函数图样与相互作用情形下的图样完全相反。
The dynamics and the noise correlations of one-dimensional anyons are investigated. Then the exact solutions are used to derive the explicit formulae of the noise correlations for both the non-interacting and interacting anyons released from a regular array. For the non-interacting anyons, interpolating between the known results of Bose and Fermi gas. For the interacting anyons, apart from the anyonic statistics, the Hamiltonian also exhibits dynamical interactions. Thus the noise correlations for the interacting anyons have a number of features that distinguish it from the non-interacting problem. A set of line-shapes appear in the noise correlations due to the distribution of scattering phases. The sign and location of the line-shape depend srongly on the interaction strength and the statistical parameter. In the Tonks-Giradeau limit, the anyonic correlations reverse the noise the non-interacting cases