Random walks on finite lattice tubes

Abstract

Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a random walk will visit a particular lattice site before being absorbed. Results are obtained for lattice tubes of arbitrary size and each of the regular lattice types; square, triangular and honeycomb. The results include an adjustable parameter to model the effects of strain, such as surface curvature, on the surface diffusion. Results for the triangular lattice tubes and the honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag carbon nano-tubes with open ends.

arXiv comment22 pages, 4 figures

References in corpus (2)

• Exact solution for random walks on the triangular lattice with absorbing boundaries
• Directed random walk in adsorbed monolayer

Cited by in corpus (6)

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