Class of solvable reaction-diffusion processes on Cayley tree

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. $\circ \circ \to \bullet \circ$, $\circ \circ \to \bullet \bullet$ and $\circ \bullet \to \bullet \bullet$, and in the second model, only the diffusion process $\bullet \circ \to \circ \bullet$ exists. For the first model, the probabilities $P_l(m;t)$, of finding $m$ particles on $l$-th shell of Cayley tree, have been found exactly, and for the second model, the functions $P_l(1;t)$ have been calculated. It has been shown that these are the only integrable models, if one restricts himself to $L+1$-shell probabilities $P(m_0,m_1,...,m_L;t)$s.

9 pages, to be appeared in Physica A

References in corpus (6)

• The Asymmetric Avalanche Process
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• Exactly solvable models through the generalized empty interval method, for multi-species interactions
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Cited by in corpus (6)

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• Growth models on the Bethe lattice
• Cooperative sequential adsorption models on a Cayley tree: analytical results and applications
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Autonomous models on a Cayley tree
• Extracting the parton distribution functions evolution equations using the stochastic modeling in the non-equilibrium statistical mechanics