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Study of anomalous kinetics of the annihilation reaction A + A → Ø

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Abstract

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 → Ø at and below its critical dimension dc = 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 ∼ 2 using a two-parameter expansion in ε and Δ, where ε is the deviation from the Kolmogorov scaling parameter and Δ 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.

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Authors and Affiliations

  1. Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia

    M. Hnatich & T. Lučivjanský

  2. Faculty of Sciences, Šafarik University, Košice, Slovakia

    M. Hnatich & T. Lučivjanský

  3. National Defence University, Helsinki, Finland

    J. Honkonen

Authors
  1. M. Hnatich
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  2. J. Honkonen
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  3. T. Lučivjanský
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Corresponding author

Correspondence to M. Hnatich.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 169, No. 1, pp. 137–145, October, 2011.

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Hnatich, M., Honkonen, J. & Lučivjanský, T. Study of anomalous kinetics of the annihilation reaction A + A → Ø. Theor Math Phys 169, 1481–1488 (2011). https://doi.org/10.1007/s11232-011-0124-9

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  • DOI: https://doi.org/10.1007/s11232-011-0124-9

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