For a free particle that non-relativistically moves on a curved surface, there are curvature-induced quantum potentials that significantly influence the surface quantum states, but the experimental results in topological insulators, whenever curved or not, indicate no evidence of such a potential, implying that there does not exist such a quantum potential for the relativistic particles, constrained on the surface or not. Within the framework of Dirac quantization scheme, we demonstrate a general result that for a Dirac fermion on a two-dimensional curved surface of revolution, no curvature-induced quantum potential is permissible.
From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
离散时间量子行走（英语：Discrete time Quantum Walk，QW）是一种通过局域幺正驱动晶格上单个粒子演化的算子。一些量子阱承认，作为它们的连续极限，一个著名的物理方程。在arXiv：1803.01015中，量子阱位于蜂窝和三角晶格上，并模拟狄拉克方程。我们在这个量子阱的晶格上应用时空坐标变换，并证明它等价于引入时空依赖的局域幺正-同时保持晶格固定。通过利用这种对偶性的变化之间的几何，并在本地幺正的变化，我们表明，时空依赖量子阱模拟狄拉克方程在$(2+1)$维弯曲时空。有趣的是，这种对偶性主要依赖于蜂窝晶格和三角晶格的三个优选方向的非线性独立性：同样的构造对于正方形晶格会失败。在实践层面上，这一结果打开了通过不同种类的晶格上的量子行走来模拟弯曲流形上的场论的可能性。
Hearing the shape of a Dirac drum: Dual quantum Hall states on curved surfaces
Institut für Theoretische Physik, Universität Regensburg（雷根斯堡大学理论物理研究所）；Department of Physics and Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University（国立成功大学物理系量子前沿研究与技术中心）；Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所）；SPEC, CEA, CNRS, Université Paris-Saclay（巴黎萨克雷大学CEA-CNRS SPEC实验室）
Landau levels in curved space realized in strained graphene
Rudolf Peierls Centre for Theoretical Physics（鲁道夫·皮尔斯理论物理中心）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克，巴斯克科学基金会）；Brown Theoretical Physics Center and Department of Physics, Brown University（布朗大学布朗理论物理中心及物理系）
