  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.
