Diffusion on a heptagonal lattice

Details Diffusion on a heptagonal lattice Diffusion on a heptagonal lattice

2008-07-14

arxiv.org/abs/0807.2089v1

Physical Review E 77, 022104 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 6 figures

Scientific paper

10.1103/PhysRevE.77.022104

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.

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