Exactly solvable models through the empty interval method, for more-than-two-site interactions

Abstract

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E_n(t)$'s, 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-neighbor interaction is studied.

19 pages, LaTeX2e

References in corpus (5)

• Phase transition of the one-dimensional coagulation-production process
• Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions
• Exactly solvable models through the empty interval method
• On the solvable multi-species reaction-diffusion processes
• Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model

Cited by in corpus (9)

• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Reaction fronts in stochastic exclusion models with three-site interactions
• Models solvable through the empty-interval method
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Exactly solvable reaction diffusion models on a Cayley tree
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems
• Autonomous models solvable through the full interval method
• The spectrum and the phase transition of models solvable through the full interval method