# Diffusion–annihilation dynamics in one spatial dimension

@article{Santos1996DiffusionannihilationDI, title={Diffusion–annihilation dynamics in one spatial dimension}, author={Jaime E Santos and Gunter M. Schutz and Robin B. Stinchcombe}, journal={Journal of Chemical Physics}, year={1996}, volume={105}, pages={2399-2407} }

We discuss a reaction–diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with rates (1±η)/2 to the right or left nearest neighbor site if it is vacant, and annihilate with rate one if it is occupied. The representation of an uncorrelated random initial state in terms of free fermions allows the calculation of multiple time‐dependent higher order correlation functions of the local density. We…

## 18 Citations

Integrable dissipative exclusion process: Correlation functions and physical properties.

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A one-parameter generalization of the symmetric simple exclusion process on a one-dimensional lattice where annihilation and creation of pairs can occur and the variance of the lattice current is computed for a finite-size system.

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A single species reaction diffusion system on a two-dimensional lattice where the particles A are biased to move towards their nearest neighbors and annihilate as they meet and the results indicate the presence of a continuous phase transition at the diffusive point.

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The kinetics of the q species pair annihilation reaction (Ai + Aj → ∅ for 1 ≤ i < j ≤ q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time…

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Recent advances in the theory of non-equilibrium systems are reviewed. The emphasis is on collective behaviour, particularly non-equilibrium stochastic dynamics and steady state phase transitions.…

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