Bulk-edge correspondence of classical diffusion phenomena - Tsuneya Yoshida; Yasuhiro Hatsugai (Scientific Reports, 2021)
Abstract 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 $$π $$ π cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.