M Khorrami et al 2003 J. Phys. A: Math. Gen. 36 345 doi:10.1088/0305-4470/36/2/304
M Khorrami1,4, A Aghamohammadi2,4 and M Alimohammadi3
Show affiliationsSingle-species reaction–diffusion systems on a one-dimensional lattice are considered, in which more than two neighbouring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for En(t), the probability that n consecutive sites are empty at time t. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbour interaction is studied.
02.50.-r Probability theory, stochastic processes, and statistics
82B23 Exactly solvable models; Bethe ansatz
35K57 Reaction-diffusion equations
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 2 (17 January 2003)
Received 20 March 2002, in final form 16 October 2002
Published 17 December 2002
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