Exact two-time correlation and response functions in the one-dimensional coagulation–diffusion process by the empty-interval method
Year: 2011
Type: article
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 one if two particles meet. The exact two-time correlation and response functions in the one-dimensional coagulation–diffusion process are derived from a generalization of the empty-interval 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 long-time ageing regime. A new generalized fluctuation-dissipation ratio with a universal and finite limit is proposed.
Authors: Xavier Durang, Jean-Yves Fortin, Malte Henkel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2139307095