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Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers
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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). . doi:10.1103/PhysRevE.70.036111
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Official URL: http://dx.doi.org/10.1103/PhysRevE.70.036111
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=2d. 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 oneloop 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:  1063651X  
Official Date:  September 2004  
Dates: 


Volume:  70  
Number:  3 Part 2  
Number of Pages:  9  
Page Range:    
Identifier:  10.1103/PhysRevE.70.036111  
Publication Status:  Published 
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