UNSPECIFIED. (2004) Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers. PHYSICAL REVIEW E, 70 (3 Part 2). -. ISSN 1063-651X

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Abstract

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda(c) and annihilation at rate lambda(a). The test particle is annihilated at rate lambda' on coming into contact with the other particles. The survival probability decays algebraically with time as t(-theta). The exponent theta in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d. It is shown to be universal, independent of lambda('), and to depend only on delta, the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda(a)/lambda(c). In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the logarithmic corrections are nonuniversal. The one-loop answer for theta in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda(a)/lambda(c). The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Journal or Publication Title:	PHYSICAL REVIEW E
Publisher:	AMERICAN PHYSICAL SOC
ISSN:	1063-651X
Date:	September 2004
Volume:	70
Number:	3 Part 2
Number of Pages:	9
Page Range:	-
Identification Number:	10.1103/PhysRevE.70.036111
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/7947

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