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

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

2010-12-21

arxiv.org/abs/1012.4724v1

J. Stat. Mech. P02030 (2011)

Physics

Condensed Matter

Statistical Mechanics

31 pages, submitted to J.Stat.Mech

Scientific paper

10.1088/1742-5468/2011/02/P02030

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.

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