Spatial fluctuations of a surviving particle in the trapping reaction

L Anton, Richard Blythe, A J Bray

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Abstract / Description of output

We consider the trapping reaction, A + B --> B, where A and B particles have a diffusive dynamics characterized by diffusion constants D-A and D-B. The interaction with B particles can be formally incorporated in an effective dynamics for one A particle as was recently shown by Bray et al (2003 Phys. Rev. E 67 060102). We use this method to compute, in space dimension d = 1, the asymptotic behaviour of the spatial fluctuation, (z(2)(t))(1/2), for a surviving A particle in the perturbative regime, D-A/D-B much less than 1, for the case of an initially uniform distribution of B particles. We show that, for t much greater than 1, (Z(2)(t))(1/2) alpha t(phi) with phi = 1/4. By contrast, the fluctuations of paths constrained to return to their starting point at time t grow with the larger exponent 1/3. Numerical tests are consistent with these predictions.

Original languageEnglish
Pages (from-to)133-144
Number of pages12
JournalJournal of Physics A: Mathematical and General
Issue number1
Publication statusPublished - 7 Jan 2005

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