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Multiscaling of correlation functions in single species reaction-diffusion systems
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UNSPECIFIED (2006) Multiscaling of correlation functions in single species reaction-diffusion systems. PHYSICAL REVIEW E, 73 (5 Part 1). -. doi:10.1103/PhysRevE.73.051103 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.73.051103
Abstract
We derive the multi-scaling of probability distributions of multi-particle configurations for the binary reaction-diffusion system A+A ->subset of in d <= 2 and for the ternary system 3A ->subset of in d=1. For the binary reaction we find that the probability P-t(N,Delta V) of finding N particles in a fixed volume element Delta V at time t decays in the limit of large time as (ln t/t)(N)(ln t)(-N(N-1)/2) for d=2 and t(-Nd/2)t(-N(N-1)epsilon/4+)O((epsilon 2)) for d < 2. Here epsilon=2-d. For the ternary reaction in one dimension we find that P-t(N,Delta V)similar to(Lnt/t)(N/2)(Ln t)(-N(N-1)(N-2)/6). The principal tool of our study is the dynamical renormalization group. We compare predictions of epsilon expansions for P-t(N,Delta V) for a binary reaction in one dimension against the exact known results. We conclude that the epsilon corrections of order two and higher are absent in the previous answer for P-t(N,Delta V) for N=1,2,3,4. Furthermore, we conjecture the absence of epsilon(2) corrections for all values of N.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Journal or Publication Title: | PHYSICAL REVIEW E | ||||
Publisher: | AMERICAN PHYSICAL SOC | ||||
ISSN: | 1539-3755 | ||||
Official Date: | May 2006 | ||||
Dates: |
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Volume: | 73 | ||||
Number: | 5 Part 1 | ||||
Number of Pages: | 10 | ||||
Page Range: | - | ||||
DOI: | 10.1103/PhysRevE.73.051103 | ||||
Publication Status: | Published |
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