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

TL;DR

This paper derives exact two-time correlation and response functions for the one-dimensional coagulation-diffusion process using the empty-interval-particle method, revealing dynamical scaling and a universal fluctuation-dissipation ratio.

Contribution

It introduces a novel application of the empty-interval-particle method to obtain exact two-time functions and analyzes their scaling and fluctuation-dissipation properties.

Findings

Exact expressions for two-time correlation functions

Analysis of dynamical scaling in ageing regime

Proposal of a universal fluctuation-dissipation ratio

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.