随机系统中物质拓扑相的分类
Classification of topological phases of matter in stochastic systems
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中文总结 AI 辅助
本文针对随机系统中的拓扑相，提出新的同伦方法和点间隙重定义，发现仅无对称性和伪厄米性两类稳健，并确定其非平凡拓扑相的维度与群结构，为活跃物质提供预测框架。
中文摘要 AI 辅助
物质的拓扑相支持受噪声和扰动保护的边缘态，其对称性和维度支持此类相的分类已在量子系统和类似平台中发展。虽然拓扑相也已在随机系统中被发现，并被提出作为生化过程的机制，但与其马尔可夫约束一致的分类仍然缺乏，阻碍了对新场景的推广。这些约束改变了矩阵空间，使得先前的分类方法无法应用，同时产生了新的性质，如非平凡拓扑相必须是非厄米的。我们引入了新方法，包括一种新的同伦方法和点间隙的重新定义，并发现只有两个对称类保持稳健：无对称性和伪厄米性。在这些对称类中，我们确定了具有非平凡拓扑相的维度及其群结构，为预测活跃和生命物质中的稳健行为创建了一个严格的框架。
英文摘要
Topological phases of matter support edge states protected from noise and perturbations, and the classification of which symmetry and dimension support such phases was developed for quantum systems and analogous platforms. While topological phases have also been discovered in stochastic systems and posited as mechanisms for biochemical processes, a classification consistent with their Markovian constraints remains lacking, impeding generalization to new scenarios. These constraints alter the matrix space preventing the application of previous classification methods, while hosting new properties such as the necessity of non-Hermiticity for non-trivial topological phases. We introduce new methods including a new homotopy approach and redefinition of the point gap and find that only two symmetry classes remain robust: no symmetry and pseudo-Hermiticity. In these symmetry classes, we identify the dimensions with topologically non-trivial phases and their group structure, creating a rigorous framework for predicting robust behavior in active and living matter.
发表机构
- Center for Theoretical Biological Physics, Rice University（理论生物物理中心，莱斯大学）
- Department of Physics and Astronomy, Rice University（物理学与天文学系，莱斯大学）
机构由 AI 辅助整理，请以论文原文为准。
