Bulk-edge correspondence of classical diffusion phenomena

TL;DR

This paper reveals that classical diffusion systems can exhibit topological bulk-edge correspondence, with robust edge states protected by winding numbers, demonstrated through discretized models and numerical simulations.

Contribution

It introduces the concept of topological phenomena in diffusive systems, showing the emergence of protected edge states and novel localized diffusive behavior.

Findings

Robust edge states exist in diffusive systems protected by winding numbers.

Temperature distribution can be localized at edges due to topological effects.

Numerical simulations confirm the presence of topologically protected edge phenomena.

Abstract

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 $\pi$ cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.