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arXiv · 0807.2089

Diffusion on a heptagonal lattice

Seung Ki Baek·Su Do Yi·Beom Jun Kim
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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.

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Seung Ki Baek, Su Do Yi, Beom Jun Kim. 2008-07-14. Diffusion on a heptagonal lattice. https://doi.org/10.1103/physreve.77.022104

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