论文标题
SU（3）截短的Wigner近似，用于强烈相互作用的Bose气体
SU(3) truncated Wigner approximation for strongly interacting Bose gases
论文作者
论文摘要
我们开发和利用SU（3）截短的Wigner近似（TWA），以分析光学晶格中强相互作用的Bose气体的远程平衡量子动力学。具体而言，我们在任意填充因子上明确表示与SU（3）矩阵有关的局部希尔伯特空间的任意填充因子。此外，我们为SU（3）TWA引入了一种离散的Wigner采样技术，并检查其性能以及SU（3）TWA的性能，并具有连续的Wigner函数的高斯近似值。我们将这两种方法的输出与有关玻色的动力学的精确计算直接比较，在单位填充较小的尺寸和具有较大尺寸的完全连接的Spin-1模型的动态。我们表明，这两种方法都可以在$ \ hbar/（jz）$的时间表上定量捕获量子动态，其中$ j $和$ z $表示跳高能量和协调号。我们将两种SU（3）TWA应用于Bose-Hubbard模型的两点相关函数的动态扩散，并在具有较大系统尺寸的正方形晶格上，这已经在最近的实验中进行了测量。这些理论和实验之间的明显偏差表明，在我们对SU（3）TWA的表述中不直接的空间不均匀性的效果的适当包含是必要的。
We develop and utilize the SU(3) truncated Wigner approximation (TWA) in order to analyze far-from-equilibrium quantum dynamics of strongly interacting Bose gases in an optical lattice. Specifically, we explicitly represent the corresponding Bose--Hubbard model at an arbitrary filling factor with restricted local Hilbert spaces in terms of SU(3) matrices. Moreover, we introduce a discrete Wigner sampling technique for the SU(3) TWA and examine its performance as well as that of the SU(3) TWA with the Gaussian approximation for the continuous Wigner function. We directly compare outputs of these two approaches with exact computations regarding dynamics of the Bose--Hubbard model at unit filling with a small size and that of a fully-connected spin-1 model with a large size. We show that both approaches can quantitatively capture quantum dynamics on a timescale of $\hbar/(Jz)$, where $J$ and $z$ denote the hopping energy and the coordination number. We apply the two kinds of SU(3) TWA to dynamical spreading of a two-point correlation function of the Bose--Hubbard model on a square lattice with a large system size, which has been measured in recent experiments. Noticeable deviations between the theories and experiments indicate that proper inclusion of effects of the spatial inhomogeneity, which is not straightforward in our formulation of the SU(3) TWA, may be necessary.
