论文标题
$ n $ - tonks-girardeau煤气的体相关
$n$-body Correlation of Tonks-Girardeau Gas
论文作者
论文摘要
对于众所周知的指数复杂性，计算一般多体波函数的相关函数是一个巨大的挑战。我们调查了托克 - 吉拉多（TG）气体的基态$ n $ th阶相关功能。基于游离费米子和玻色纤维映射方法的波函数，我们获得了TG气体的确切基态波函数。利用Vandermonde依据和Toeplitz矩阵的属性，$ n $ th阶相关函数被表达为$（n-n）$ - 订购toeplitz clategents，其元素的积分取决于2 $（n-n）$符号函数，并且可以通过分析进行分析计算。通过将域$ [0,2π] $的积分放在几个独立域上的积分的总和中，我们最终获得了Toeplitz矩阵元素的明确形式。作为应用，我们推断出降低的两体密度矩阵的简洁公式并讨论其特性。绘制了相应的天然轨道及其职业分布。此外，我们给出了降低的三体密度矩阵的简洁公式，并讨论其特性。结果表明，在连续的第二个测量值中，原子出现在原子在第一个测量中具有最大概率的区域。
For the well-known exponential complexity it is a giant challenge to calculate the correlation function for general many-body wave function. We investigate the ground state $n$th-order correlation functions of the Tonks-Girardeau (TG) gases. Basing on the wavefunction of free fermions and Bose-Fermi mapping method we obtain the exact ground state wavefunction of TG gases. Utilizing the properties of Vandermonde determinant and Toeplitz matrix, the $n$th-order correlation function is formulated as $(N-n)$-order Toeplitz determinant, whose element is the integral dependent on 2$(N-n)$ sign functions and can be computed analytically. By reducing the integral on domain $[0,2π]$ into the summation of the integral on several independent domains, we obtain the explicit form of the Toeplitz matrix element ultimately. As the applications we deduce the concise formula of the reduced two-body density matrix and discuss its properties. The corresponding natural orbitals and their occupation distribution are plotted. Furthermore, we give a concise formula of the reduced three-body density matrix and discuss its properties. It is shown that in the successive second measurements, atoms appear in the regions where atoms populate with the maximum probability in the first measurement.
