中文摘要：

基于满足周期性边界条件的一维光晶格模型,分别研究遵从玻色-爱因斯坦统计的玻色系统、遵从费米-狄拉克统计的费米系统以及硬核玻色系统下的两粒子关联、关联涨落、平均粒子数分布以及动力学演化等问题,计算量子统计性质和相互作用强度（排斥）对两粒子量子行走（独立行走和绑定行走）的影响。结果表明,在坐标空间中,随着时间的增大,粒子向晶格边缘移动,尤其当相互作用为零时,玻色系统的两粒子关联虽呈现聚束现象,却展示出一种与众不同的对称———输入输出对称,而费米（硬核玻色）系统的两粒子关联呈现类似环类的空间分布。随着排斥相互作用的增大,3系统都会出现两粒子绑定行走行为,在强相互作用下,研究的物理量（粒子关联、关联涨落和平均粒子数分布）在3系统中几乎相同；在动量空间中,玻色系统呈典型的聚束现象,费米系统呈反聚束现象,硬核玻色系统呈聚束现象。计算结果为实验上研究不同系统（玻色、费米和硬核玻色）的物理性质提供了依据,并佐证了实验上排斥相互作用下束缚态产生的实验结果。

英文摘要：

Based on one-dimensional lattices with periodic boundary conditions, we investigate the two-particle correlations, the correlation fluctuations, and the density distributions as well as the dynamic evolutions of the bosonic system governed by Bose-Einstein statistics, the fermionic system governed by Fermi-Dirac statistics, and the hard-core bosonic system, respectively. The dependences of independent walking and co-walking for two interacting particles on both quantum statistics and interaction strength are calculated. The results show that the particles move to the edge of the lattice with the increase of time in position space. Specifically, for zero interaction, bosonic correlations exhibit bunching but with a specific “in-out” correlation symmetry, while the fermionic correlations （ hard-core bosonic correlations ） are transformed into a ring-like pattern. However, two particles in the bosonic system and fermionic system （ hard-core bosonic system） start to occupy adjacent lattice sites separated by one site and stick together when they are co-walking with increasing interaction. The correlations in the three systems are nearly the same under strong interactions and are the same with correlation fluctuations and density distributions. In momentum space, the quantum statistical natures for two bosonic （ hard-core bosonic） walkers and two fermionic walkers result in the emergence of bunching and anti-bunching in two-particle quantum walks （ QWs） , respectively. In short, the results pave the way for exploring quantum statistics and can be used as evidences for the repulsively bound state observed experimentally.