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.

5 pages, 6 figures

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• Percolation on hyperbolic lattices
• Quantum phase transitions of interacting bosons on hyperbolic lattices
• Curvature-induced frustration in the $XY$ model on hyperbolic surfaces
• Bootstrap percolation and kinetically constrained models on hyperbolic lattices
• Phase transition of $q$-state clock models on heptagonal lattices
• Percolation Thresholds in Hyperbolic Lattices