We show an implementation of a $\kappa$-deformed Dirac equation in tight-binding arrays of photonic waveguides. This is done with a special configuration of couplings extending to second-nearest neighbors. Geometric manipulations can control these evanescent couplings. A careful study of wave packet propagation is presented, including the effects of deformation parameters on Zitterbewegung or trembling motion. In this way, we demonstrate how to emulate the effects of a flat noncommutative spacetime—i.e., $\kappa$-Minkowski spacetime—in simple experimental setups.

中文翻译：

---

κ-变形狄拉克方程的光子实现

我们展示了一个实现 $\kappa$- 光子波导紧束缚阵列中的变形狄拉克方程。这是通过扩展到第二近邻的耦合的特殊配置来完成的。几何操作可以控制这些渐逝耦合。对波包传播进行了仔细研究，包括变形参数对Zitterbewegung或颤动运动的影响。通过这种方式，我们演示了如何模拟平坦的非对易时空的影响——即，$\kappa$-闵可夫斯基时空——在简单的实验设置中。