Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method

Abstract

The long-time dynamics of reaction-diffusion processes in low dimensions is dominated by fluctuation effects. The one-dimensional coagulation-diffusion process describes the kinetics of particles which freely hop between the sites of a chain and where upon encounter of two particles, one of them disappears with probability one. The empty-interval method has, since a long time, been a convenient tool for the exact calculation of time-dependent particle densities in this model. We generalise the empty-interval method by considering the probability distributions of two simultaneous empty intervals at a given distance. While the equations of motion of these probabilities reduce for the coagulation-diffusion process to a simple diffusion equation in the continuum limit, consistency with the single-interval distribution introduces several non-trivial boundary conditions which are solved for the first time for arbitrary initial configurations. In this way, exact space-time-dependent correlation functions can be directly obtained and their dynamic scaling behaviour is analysed for large classes of initial conditions.

Latex2e, 32 pages, 3 figures

References in corpus (4)

• Ageing phenomena without detailed balance: the contact process
• Ageing in the critical contact process: a Monte Carlo study
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• Crossover properties of a one-dimensional reaction-diffusion process with a transport current
• Fractional diffusion equations interpolate between damping and waves
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Exact correlation functions in particle-reaction models with immobile particles
• Aging processes in reversible reaction-diffusion systems: Monte Carlo simulations
• Reaction-diffusion on the fully-connected lattice: $A+A\to A$
• Autonomous models solvable through the full interval method
• Analytical results for a coagulation/decoagulation model on an inhomogeneous lattice
• The spectrum and the phase transition of models solvable through the full interval method
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain