Feynman-type representation of the scattering matrix on the line via a discrete-time quantum walk
Feynman-type representation of the scattering matrix on the line via a discrete-time quantum walk
复制标题
通过离散时间量子行走对线上散射矩阵进行费曼型表示
DOI：
--
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
K. Higuchi
中科院分区：
文献类型：
--
作者：
K. Higuchi
本文的目的是在散射问题中将整数集\(Z\)上的离散量子行走与实数集\(R\)上的连续薛定谔算子联系起来。\(Z\)中的每个点都与一个势垒相关联，并且量子行走的硬币算子由势垒两侧经典允许区域上WKB解的基之间的转移矩阵所确定。这种对应关系使我们能够将薛定谔算子散射矩阵的每个元素表示为与量子行走者路径相关的概率幅的可数和。特别地，在半经典极限下，势垒顶部散射对应于哈达玛行走。
The aim of this article is to relate the discrete quantum walk on Z with the continuous Schrödinger operator on R in the scattering problem. Each point of Z is associated with a barrier of the potential, and the coin operator of the quantum walk is determined by the transfer matrix between bases of WKB solutions on the classically allowed regions of both sides of the barrier. This correspondence enables us to represent each entry of the scattering matrix of the Schrödinger operator as a countable sum of probability amplitudes associated with the paths of the quantum walker. In particular, the barrier-top scattering corresponds to the Hadamard walk in the semiclassical limit.
作为范式的韦伯方程应用于势垒顶部散射
影响因子：
1
作者：
Costin, Rodica;Park, Hyejin;Schlag, Wilhelm
通讯作者：
Schlag, Wilhelm