论文标题
通过路径计数方法进行量子步行的广义本征函数
Generalized eigenfunctions for quantum walks via path counting approach
论文作者
论文摘要
我们考虑一维两国量子步行的时间演化算子的时间无关的散射理论。与位置依赖性量子行走相关的散射矩阵自然出现在广义本征函数的空间无穷大的渐近行为中。广义本征函数的渐近行为是与自由量子行走相关的绿色功能的明确表达的结果。当位置依赖性量子步行是自由量子步行的有限秩扰动时，我们通过计数量子步行者的路径来得出散射矩阵的一种组合构建体。我们还提到了有关隧道效应的一些评论。
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic behavior at spatial infinity of generalized eigenfunctions. The asymptotic behavior of generalized eigenfunctions is a consequence of an explicit expression of the Green function associated with the free quantum walk. When the position-dependent quantum walk is a finite rank perturbation of the free quantum walk, we derive a kind of combinatorial constructions of the scattering matrix by counting paths of quantum walkers. We also mention some remarks on the tunneling effect.
