Scientific Reports (Jan 2021)

Bulk-edge correspondence of classical diffusion phenomena

  • Tsuneya Yoshida,
  • Yasuhiro Hatsugai

DOI
https://doi.org/10.1038/s41598-020-80180-w
Journal volume & issue
Vol. 11, no. 1
pp. 1 – 7

Abstract

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