Multispecies reaction-diffusion systems

Abstract

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.

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

“…It was shown that these models may exhibit dynamic and static phase transitions. The same idea has been generalized to multi-species models [22] in one dimension with two-site interactions. There, conditions have been obtained that the Hamiltonian should satisfy in order that the evolution equation for correlation functions be closed.…”

“…Different methods have been used to study these models, including analytical and asymptotic methods, mean field methods, and large-scale numerical methods. Systems with more than one species have also been studied [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Many of the arguments are based on simulation results.…”

Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems

“…These are the autonomous systems. For a system with the Hamiltonian H 0 to be autonomous, following constraints hold among the reaction rates nd their reaction rates [27][28][29].…”

“…There, for these models the average particle-number in each site was obtained exactly. In [28,29], this has been generalized to multi-species systems and more-thantwo-site interactions.…”

Phase transition in an asymmetric generalization of the zero-temperature Glauber model

“…Moreover, solving one-dimensional systems should in principle be easier. Exact results for some models on a one-dimensional lattice have been obtained, for example in [1][2][3][4][5][6][7][8][9][10][11][12]. Different methods have been used to study these models, including analytical and asymptotic methods, mean field methods, and large-scale numerical methods.…”