Two-species annihilation with drift: A model with continuous concentration-decay exponents

Kinetics of the bosonic A+B-->0 reaction with on-site attractive interaction

We investigate kinetics of the uniformly driven bosonic A+B-->0 reaction with on-site attractive interaction in one dimension. In this model, n(i)(lambda) particles from a site with n(i) particles are driven to the right. When particles of opposite species occupy the same site, the reaction takes place instantaneously. Since n(i)(lambda)<n(i) for lambda<1, lambda controls the on-site attractive interaction between like particles. The lambda=0 case corresponds to the hard-core (HC) particle model. With equal initial densities of both species, we numerically confirm that the scaling behaviors of density and lengths are the same as those of the uniformly driven HC particle system. Especially the domain length l satisfies the power law l approximately t(2/3). The kinetics of the reaction is independent of lambda as long as lambda<1. The lambda -independent kinetics results from the lambda -independent collective motions of single species domains.

Continuously varying exponents in A+B-->0 reaction with long-ranged attractive interaction

We investigate kinetics of A+B-->0 reaction with long-range attractive interaction V(r) approximately -r(-2sigma) between A and B or with drift velocity v approximately r(-sigma) in one dimension, where r is the closest distance between A and B . It is analytically shown that dynamical exponents for density of particles (rho) and size of domains (l) continuously vary with sigma when sigma < sigma(c) = 1/2 , while that for the distance between adjacent opposite species (l(AB)) varies when sigma < sigma(c)AB = 7/6 . For sigma > sigma(c)AB diffusive motions dominate the kinetics. These anomalous behaviors with the two crossover values of sigma are supported by numerical simulations.

First-passage method for the study of the efficiency of a two-channel reaction on a lattice

We study the efficiency of a two-channel reaction between two walkers on a finite one-dimensional periodic lattice. The walkers perform a combination of synchronous and asynchronous jumps on the lattice and react instantaneously when they meet at the same site (first channel) or upon position exchange (second channel). We develop a method based on a conditional first-passage problem to obtain exact results for the mean number of time steps needed for the reaction to take place as well as for higher order moments. Previous results obtained in the framework of a difference equation approach are fully confirmed, including the existence of a parity effect. For even lattices the maximum efficiency corresponds to a mixture of synchronous events and a small amount of asynchronous events, while for odd lattices the reaction time is minimized by a purely synchronous process. We provide an intuitive explanation for this behavior. In addition, we give explicit expressions for the variance of the reaction time. The latter displays a similar even-odd behavior, suggesting that the parity effect extends to higher order moments.

Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions

Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for the closedness of the evolution equations of the n-point functions are obtained. The average numbers of the particles at each site for one species and three-site interactions, and its generalization to the more-than-three-site interactions, are explicitly obtained. Generalizations of the Glauber model in different directions, using generalized rates, generalized numbers of states at each site, and generalized numbers of interacting sites, are also investigated.

Path-integral formulation of stochastic processes for exclusive particle systems

We present a systematic formalism to derive a path-integral formulation for hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE), and the stochastic differential equation (SDE) is derived by connecting these coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto field theory using the path integral, giving the field-theoretic action, which may be analyzed by the renormalization group method. We apply this formalism to a two-species reaction-diffusion system with drift, finding a universal decay exponent for the long-time behavior of the average concentration of particles in arbitrary dimension.

Multispecies reaction-diffusion systems

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.