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A class of solvable reaction–diffusion processes on a Cayley tree

Author

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  • Alimohammadi, M.
  • Olanj, N.

Abstract

Considering the most general one-species reaction–diffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. ∘∘→•∘, ∘∘→•• and ∘•→••, and in the second model, only the diffusion process •∘→∘• exists. For the first model, the probabilities Pl(m;t), of finding m particles on the lth shell of the Cayley tree, have been found exactly, and for the second model, the functions Pl(1;t) have been calculated. It has been shown that these are the only integrable models if one restricts consideration to the L+1-shell probabilities P(m0,m1,…,mL;t).

Suggested Citation

  • Alimohammadi, M. & Olanj, N., 2010. "A class of solvable reaction–diffusion processes on a Cayley tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1549-1554.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:8:p:1549-1554
    DOI: 10.1016/j.physa.2009.12.045
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