Physics – Condensed Matter
Scientific paper
1993-11-30
J. Phys. A 27, 2633 (1994)
Physics
Condensed Matter
24 pages (harvmac), 8 figures appended, OUTP-93-39S
Scientific paper
10.1088/0305-4470/27/8/004
The diffusion-controlled reaction $kA\rightarrow\emptyset$ is known to be strongly dependent on fluctuations in dimensions $d\le d_c=2/(k-1)$. We develop a field theoretic renormalization group approach to this system which allows explicit calculation of the observables as expansions in $\epsilon^{1/(k-1)}$, where $\epsilon=d_c-d$. For the density it is found that, asymptotically, $n\sim A_k t^{-d/2}$. The decay exponent is exact to all orders in $\epsilon$, and the amplitude $A_k$ is universal, and is calculated to second order in $\epsilon^{1/(k-1)}$ for $k=2,3$. The correlation function is calculated to first order, along with a long wavelength expansion for the second order term. For $d=d_c$ we find $n \sim A_k (\ln t/t)^{1/(k-1)}$ with an exact expression for $A_k$. The formalism can be immediately generalized to the reaction $kA\rightarrow\ell A$, $\ell < k$, with the consequence that the density exponent is the same, but the amplitude is modified.
No associations
LandOfFree
Renormalization Group Calculation for the Reaction $kA\rightarrow\emptyset$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Renormalization Group Calculation for the Reaction $kA\rightarrow\emptyset$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renormalization Group Calculation for the Reaction $kA\rightarrow\emptyset$ will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-687168