title: Diffusion on a heptagonal lattice.
abstract: 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.
authors: Department of Physics, BK21 Physics Research Division, and Institute of Basic Science, Sungkyunkwan University, Suwon, Republic of Korea.
authors: Seung Ki
authors: SK
authors: Baek
authors: Su Do
authors: SD
authors: Yi
authors: Beom Jun
authors: BJ
authors: Kim