Anomalous dimension in a two-species reaction–diffusion system

@article{VollmayrLee2017AnomalousDI,
  title={Anomalous dimension in a two-species reaction–diffusion system},
  author={Benjamin P. Vollmayr-Lee and Jack Hanson and R Scott McIsaac and Joshua D. Hellerick},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2017},
  volume={51}
}
We study a two-species reaction–diffusion system with the reactions A+A→(0,A) and A+B→A, with general diffusion constants DA and DB. Previous studies showed that for dimensions d⩽2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling C~BB(r… 
5 Citations

Corrigendum: Anomalous dimension in a two-species reaction–diffusion system (2018 J. Phys. A: Math. Theor. 51 034002)

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References

SHOWING 1-10 OF 29 REFERENCES

Fluctuation kinetics in a multispecies reaction-diffusion system

We study fluctuation effects in a two-species reaction - diffusion system, with three competing reactions , and . Asymptotic density decay rates are calculated for using two separate methods - the

Long range hops and the pair annihilation reaction A+A-->0: renormalization group and simulation.

  • D. Vernon
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
The renormalization group can be used to calculate the time dependence of the density of particles, and provides both an exact value for the exponent governing the decay of particles and an epsilon expansion for the amplitude of this power law.

Field Theory of Branching and Annihilating Random Walks

We develop a systematic analytic approach to the problem of branching and annihilating random walks, equivalent to the diffusion-limited reaction processes 2A → ∅ and A → (m + 1) A, where m ≥ 1.

Renormalization group calculation for the reaction kA + 0

The diffusion-controlled reaction kA + M is known IO be strongly dependent on Ruchlations in dimensions d < d. = 2/(k - 1). We develop a field-theoretic renormalization group approach to this system

TOPICAL REVIEW: Applications of field-theoretic renormalization group methods to reaction diffusion problems

We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction–diffusion problems. We first investigate the physical origin of universality

Multiscaling of correlation functions in single species reaction-diffusion systems.

The principal tool of the study is the dynamical renormalization group and it is concluded that the epsilon corrections of order two and higher are absent in the previous answer for Pt(N, Delta V) for N=1, 2, 3, 4.

Kinetics of heterogeneous single-species annihilation.

  • KrapivskyBen-NaimRedner
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
The kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different, is investigated, and the theoretical predictions compare well with both Monte Carlo simulations and time series expansions.

Persistence properties of a system of coagulating and annihilating random walkers.

This work calculates P(m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m-1) coagulations, and derives an exact nonperturbative relation between the exponents: namely delta(Q)=theta(1-Q).

Trapping reaction with mobile traps.

The Monte Carlo results for the two-species trapping reaction A+B-->B with diffusing A and B on lattices in one, two, and three dimensions are presented, showing that the asymptotic regime has not been reached, at least for d=2 and d=3.