论文标题
基塔夫模型和类似Majorana的拓扑结合状态的古典类似物
Classical analogue to the Kitaev model and Majorana-like topological bound states
论文作者
论文摘要
这项研究探讨了可能性，并提出了一种将经典的机械类似物与量子机械1D Kitaev模型合成的方法。尽管从根本上有所不同，但我们将确定在发生在经典类似系统中的两个模型之间的显着概念相似性，类似于Majorana零模式的拓扑非平凡结合状态。通过以一种让人联想到第二个量化的形式，通过对古典系统的哈密顿式进行重新阐述，我们表明，一维交错的经典机械链可以表现出与基塔耶夫的一维超导模型相似的动态特征，以及其特性结合状态。通过拓扑带结构分析和拓扑不变，进一步证实了结合状态的非平凡拓扑性质。尽管这些国家的非亚洲性质仍然是一个悬而未决的问题，但这些结果允许设想在经典机械系统中实现拓扑编织的可能性。
This study explores the possibility and presents a methodology to synthesize a classical mechanical analogue to the quantum mechanical 1D Kitaev model. While being fundamentally different, we will identify significant conceptual similarities between the two models that culminate in the occurrence, in the classical analogue system, of topologically non-trivial bound states that are akin to Majorana zero modes. By reformulating the Hamiltonian of the classical system in a form reminiscent of second quantization, we show that a 1D staggered classical mechanical chain can exhibit dynamic characteristics analogous to the Kitaev's 1D superconducting model, as well as its characteristic bound states. The non-trivial topological nature of the bound states is further confirmed by the topological band structure analysis and by the topological invariant. While the non-Abelian nature of these states remains an open question, these results allow envisioning the possibility to achieve topological braiding in classical mechanical systems.
