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We analyse the aging dynamics of the one-dimensional Fredrickson-Andersen(FA) model in the nonequilibrium regime following a low temperature quench.Relaxation then effectively proceeds via diffusion limited pair coagulation(DLPC) of mobility excitations. By employing a familiar stochastic similaritytransformation, we map exact results from the free fermion case of diffusionlimited pair annihilation to DLPC. Crucially, we are able to adapt the mappingtechnique to averages involving multiple time quantities. This relies onknowledge of the explicit form of the evolution operators involved. Exactresults are obtained for two-time correlation and response functions in thefree fermion DLPC process. The corresponding long-time scaling forms apply to awider class of DLPC processes, including the FA model. We are thus able toexactly characterise the violations of the fluctuation-dissipation theorem(FDT) in the aging regime of the FA model. We find nontrivial scaling forms forthe fluctuation-dissipation ratio (FDR) X = X(tw/t), but with a negativeasymptotic value X = -3*pi/(6*pi - 16) = -3.307. While this prevents athermodynamic interpretation in terms of an effective temperature, it is adirect consequence of probing FDT with observables that couple to activateddynamics. The existence of negative FDRs should therefore be a widespreadfeature in non mean-field systems.Comment: 39 pages, 4 figure

Ageing in one-dimensional coagulation–diffusion processes and the Fredrickson–Andersen model