A class of solvable reaction-diffusion processes on a Cayley tree |
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Authors: | M Alimohammadi N Olanj |
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Institution: | Department of Physics, University of Tehran, North Karegar Avenue, Tehran, Iran |
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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). |
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Keywords: | Reaction-diffusion processes Cayley tree Integrable models |
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