Bulk-edge correspondence of classical diffusion phenomena

We elucidate that 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 diffusive dynamics at edges. Furthermore, we discover a novel diffusion phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber pi cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.

Automated summary

This study reveals that diffusive systems can serve as a new platform for studying topological phenomena, demonstrating robust edge states protected by winding number in one- and two-dimensional systems. Furthermore, a novel diffusion phenomenon is discovered through numerical simulations, where a temperature field with a specific wavenumber cannot diffuse into the bulk due to the complete localization of edge states.