# 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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## References

SHOWING 1-10 OF 38 REFERENCES

Diffusion-annihilation in the presence of a driving field

- Physics
- 1995

We study the effect of an external driving force on a simple stochastic reaction-diffusion system in one dimension. In our model each lattice site may be occupied by at most one particle. These…

Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part I. Analytical results

- Mathematics
- 1995

We consider two single-species reaction-diffusion models on one-dimensional lattices of lengthL: the coagulation-decoagulation model and the annihilation model. For the coagulation model the system…

Diffusion-annihilation and the kinetics of the Ising model in one dimension

- Physics
- 1991

The relationship between the one-dimensional kinetic Ising model at zero temperature and diffusion-annihilation in one dimension is studied. Explicit asymptotic results for the average domain size,…

Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation

- Physics
- 1995

We report exact results for one-dimensional reaction-diffusion modelsA+A→inert,A+A→A, andA+B→inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study…

Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition

- Physics
- 1990

We solve exactly the one-dimensional diffusion-limited single-species coagulation process (A+A→A) with back reactions (A→A+A) and/or a steady input of particles (B→A). The exact solution yields not…

Multiparticle reactions with spatial anisotropy.

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

It is argued that the spatial anisotropy introduces no appreciable changes as compared to the isotropic case, and these conjectures are supported by numerical simulations for slow reaction rates.

CONCENTRATION FOR ONE AND TWO-SPECIES ONE-DIMENSIONAL REACTION-DIFFUSION SYSTEMS

- Physics
- 1995

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to…

Diffusion-limited exciton fusion reaction in one-dimensional tetramethylammonium manganese trichloride (TMMC).

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1993

At higher initial exciton densities the diffusion process, and thus the reaction rate, is significantly influenced by the heat produced in the fusion reaction, and this is supported by Monte Carlo simulations.

Equivalences between stochastic systems

- Mathematics, Physics
- 1995

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are studied. This is achieved by similarity transformations between…

Second quantization representation for classical many-particle system

- Physics
- 1976

The second quantization method is applied to classical many-particle systems. Statistical quantities such as free energy and time correlation functions are expressed in terms of creation and…