Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method

Abstract

The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles meet. The exact two-time correlation and response function in the one-dimensional coagulation-diffusion process are derived from the empty-interval-particle method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the longtime ageing regime. A new generalised fluctuation-dissipation ratio with an universal and finite limit is proposed.

31 pages, submitted to J.Stat.Mech

References in corpus (11)

• Directed percolation criticality in turbulent liquid crystals
• Experimental realization of directed percolation criticality in turbulent liquid crystals
• Ageing phenomena without detailed balance: the contact process
• Ageing in the critical contact process: a Monte Carlo study
• Non-equilibrium dynamics of spin facilitated glass models
• Aging in One-Dimensional Coagulation-Diffusion Processes and the Fredrickson-Andersen Model
• Local scale invariance in the parity conserving nonequilibrium kinetic Ising model
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Ageing in bosonic particle-reaction models with long-range transport
• Aging processes in reversible reaction-diffusion systems

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• Crossover properties of a one-dimensional reaction-diffusion process with a transport current
• 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: $A+A\to A$
• Modified stochastic fragmentation of an interval as an ageing process
• Autonomous models solvable through the full interval method
• 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