Relativistic effects and rigorous limits for discrete- and continuous-time quantum walks
Relativistic effects and rigorous limits for discrete- and continuous-time quantum walks
复制标题
DOI：
10.1063/1.2759837
复制
发表时间：
2007-08
影响因子：
1.3
通讯作者：
F. Strauch
中科院分区：
文献类型：
--
作者：
F. Strauch
通过研究离散时间和连续时间量子行走与一维狄拉克方程的一类解，分别用广义贝塞尔函数、正则贝塞尔函数和修正贝塞尔函数表示，探讨了它们之间的数学关系。建立了连接这些解决方案的严格限制。此外，对量子行走和狄拉克方程给出了新的解析和数值结果，包括纠缠、相对论局域化和波包传播，以及正常和异常的齐特比态。
The mathematical relationship between the discrete-time and continuous-time quantum walks and the one-dimensional Dirac equation is explored by studying a class of solutions for each, expressed in terms of the generalized, regular, and modified Bessel functions, respectively. Rigorous limits connecting these solutions are established. In addition, new analytical and numerical results are presented for quantum walks and the Dirac equation, including entanglement, relativistic localization and wave packet spreading, and normal and anomalous Zitterbewegung.