标题： 二维量子漫步的极限分布 显示英文标题

标题： Limit distributions of two-dimensional quantum walks

摘要： 一个关于平方格点上的离散时间量子行走模型的一参数族，其中包含Grover行走模型作为特例，被进行了分析研究。 证明了所有行走者伪速度两个分量$X_t/t$和$Y_t/t$在长时间极限$t \to \infty$下的联合矩的收敛性，并推导出了极限分布的概率密度。 确定了二维极限密度函数对量子硬币参数和量子行走者初始四组分量子比特的依赖关系。 平面上极限分布的对称性和围绕原点的局域化现象得到了完全控制。 还展示了与直接计算机模拟数值结果的比较。 显示英文摘要

摘要： One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two components of walker's pseudovelocity, $X_t/t$ and $Y_t/t$, is proved and the probability density of limit distribution is derived. Dependence of the two-dimensional limit density function on the parameter of quantum coin and initial four-component qudit of quantum walker is determined. Symmetry of limit distribution on a plane and localization around the origin are completely controlled. Comparison with numerical results of direct computer-simulations is also shown.