Geodesic
Study of anomalous kinetics of the~annihilation reaction $A+A\to\varnothing$
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 1, pp. 137-145

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Using the perturbative renormalization group, we study the influence of a random velocity field on the kinetics of the single-species annihilation reaction $A+A\to\varnothing$ at and below its critical dimension $d_c=2$. We use the second-quantization formalism of Doi to bring the stochastic problem to a field theory form. We investigate the reaction in spaces of dimension $d\sim2$ using a two-parameter expansion in $\epsilon$ and $\Delta$, where $\epsilon$ is the deviation from the Kolmogorov scaling parameter and $\Delta$ is the deviation from the space dimension $d=2$. We evaluate all the necessary quantities, including fixed points with their regions of stability, up to the second order of the perturbation theory.
Keywords: renormalization group, reaction kinetics, dimensional analysis, effective action.
Mots-clés : second quantization 
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     author = {M. Gnatich and J. Honkonen and T. Lu\v{c}ivjansk\'y},
     title = {Study of anomalous kinetics of the~annihilation reaction $A+A\to\varnothing$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {137--145},
     publisher = {mathdoc},
     volume = {169},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a12/}
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M. Gnatich; J. Honkonen; T. Lučivjanský. Study of anomalous kinetics of the~annihilation reaction $A+A\to\varnothing$. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 1, pp. 137-145. http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a12/