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