论文标题
多维量子步行：Dirac和Schrödinger颗粒的操场
Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
论文作者
论文摘要
我们提出了一个新的多维离散时间量子步行（DTQW），其连续限制是扩展的多维迪拉克方程，可以进一步映射到Schrödinger方程。我们通过两种方式表明，我们的DTQW是研究二维（2D）扩展的Dirac Hamiltonian和高阶拓扑材料的绝佳措施。首先，我们表明DTQW的动力类似于2DSchrödinger和谐振荡器的动力。其次，我们在扩展狄拉克系统的DTQW拓扑特征中发现。通过操纵硬币操作员，我们不仅可以生成标准边缘状态，还可以生成角状态。
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schrödinger equation. We show in two ways that our DTQW is an excellent measure to investigate the two-dimensional (2D) extended Dirac Hamiltonian and higher-order topological materials. First, we show that the dynamics of our DTQW resembles that of a 2D Schrödinger harmonic oscillator. Second, we find in our DTQW topological features of the extended Dirac system. By manipulating the coin operators, we can generate not only standard edge states but also corner states.
