论文标题
经典扩散现象的散装对应关系
Bulk-edge correspondence of classical diffusion phenomena
论文作者
论文摘要
我们阐明，在自然界中广泛发现的扩散系统可能是代表性拓扑现象的散装对应关系的新平台。使用离散的扩散方程式，我们证明了一个由一维系统和二维系统保护的稳健边缘状态的出现。这些拓扑边缘状态可以通过测量边缘的扩散动力学在实验上访问。此外，我们通过数值模拟蜂窝晶格系统的温度分布来发现一种新颖的扩散现象。带有波数$π$的温度场无法扩散到大体，这归因于边缘状态的完整定位。
We elucidate that the diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring the diffusive dynamics at the edges. Furthermore, we discover a novel diffusive phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $π$ cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.
