Comment on "Solution of classical stochastic one-dimensional many-body Systems"

Exact dynamics of a reaction-diffusion model with spatially alternating rates

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative "temperatures" have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time dependence are found: if both temperatures are positive, the magnetization, density, and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.

Exact multipoint and multitime correlation functions of a one-dimensional model of adsorption and evaporation of dimers

In this work, we provide a method that allows us to compute exactly the multipoint and multitime correlation functions of a one-dimensional stochastic model of dimer adsorption evaporation with random (uncorrelated) initial states. In particular, explicit expressions of the two-point non-instantaneous/instantaneous correlation functions are obtained. The long-time behavior of these expressions is discussed in detail and in various physical regimes.

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models that cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called interparticle distribution function (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model that cannot be solved directly by the conventional IPDF method and that can be viewed as a generalization of the voter model and/or as an epidemic model. We also consider the reversible diffusion-coagulation model with input of particles and determine other reaction-diffusion models that can be mapped onto the latter via suitable similarity transformations. Finally we study the problem of the propagation of a wave front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.

Correlation functions for diffusion-limited annihilation, A+A-->0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A+A-->0, is obtained analytically and explicitly, following the method of intervals. In the long-time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A+A-->A, despite differences between the two models in other statistical measures, such as the interparticle distribution function.

Two-point correlation functions of the diffusion-limited annihilation in one dimension

Two-point density-density correlation functions for the diffusive binary reaction system A+A--> phi are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from that of a recent analytical prediction of Bares and Mobilia [Phys. Rev. Lett. 83, 5214 (1999)]. An alternative expression for the asymptotic behavior is conjectured from numerical data.

Exact solution of a class of one-dimensional nonequilibrium stochastic models

We consider various one-dimensional nonequilibrium models, namely, the diffusion-limited pair-annihilation and creation model (DPAC) and its unbiased version (the Lushnikov model), the DPAC model with particle injection, as well as (biased) diffusion-limited coagulation model (DC). We study the DPAC model using an approach based on a duality transformation and the generating function of the dual model. We are able to compute exactly the density and correlation functions in the general case with arbitrary initial states. Further, we assume that a source injects particles in the system. Solving, via the duality transformation, the equations of motion of the density, and the noninstantaneous two-point correlation functions, we see how the source affects the dynamics. Finally we extend the previous results to the DC model with help of a similarity transformation.