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… 
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References

SHOWING 1-10 OF 38 REFERENCES
Diffusion-annihilation in the presence of a driving field
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
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
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
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
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.
  • Privman, Burgos, Grynberg
  • Physics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
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
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).
  • Kroon, Fleurent, Sprik
  • Physics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
TLDR
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
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
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…
...
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3
4
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