Random walks on finite lattice tubes

Details Random walks on finite lattice tubes Random walks on finite lattice tubes

2003-05-10

arxiv.org/abs/math-ph/0305023v1

Phys. Rev. E 68 (2003) 016112

Physics

Mathematical Physics

22 pages, 4 figures

Scientific paper

10.1103/PhysRevE.68.016112

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.

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