2008/02/15 by Seung Ki Baek, Sudo Yi, Su Do Yi +1 · 4 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.77.022104
published as Physical Review E 77, 022104 (2008) · 5 pages, 6 figures
openalex publication_date 2008/02/15 · arxiv created 2008/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence the displacement of a classical random walker increases linearly in time. The diffusion of a quantum particle put on the heptagonal lattice is also studied in the framework of the tight-binding model Hamiltonian, and we again find the linear diffusion like the classical random walk. A comparison with diffusion on complex networks is also made.