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 pi cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.
Highlights
We discover a novel diffusion 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
By discretizing the diffusion equation, we have shown that the diffusive dynamics of classical systems can be described by the tight-binding model of quantum systems [see Eq (3)]
Based on Fick’s law, we have introduced the discretized form of the diffusion equation, bridging the diffusive dynamics of classical systems and a tight-binding model discussed for quantum systems
Summary
Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. The discretized diffusion equation allows us to discuss the bulk-edge correspondence of diffusion phenomena for classical systems; the governing equation is expressed in a matrix form that is mathematically equivalent to a tight-binding model of a quantum system.
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