Session B22: Systems Far from Equilibrium

11:15 AM–2:15 PM, Monday, March 5, 2007
Colorado Convention Center Room: 108

Sponsoring Unit: GSNP
Chair: Beate Schmittman, Virginia Polytechnic Institute and State University

Abstract ID: BAPS.2007.MAR.B22.9

Abstract: B22.00009 : Renormalization Group Treatment of the Trapping Reaction

12:51 PM–1:03 PM

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  Jack Hanson
    (Rutgers University)

  Scott McIsaac
    (Rice University)

  Benjamin Vollmayr-Lee
    (Bucknell University)

We consider the trapping reaction $A+B\to A$, with diffusing traps ($A$) and particles ($B$), where the traps additionally undergo either an annihilation ($A+A\to\emptyset$) or coalescence ($A+A\to A$) reaction. This two-species reaction-diffusion system exhibits asymptotic power law decays in both the trap and particle densities, and simple scaling in the trap-trap ($AA$) and particle-trap ($AB$) correlation functions. However, simulations indicate the induced particle-particle correlations scale as $C_{BB}(x,t) = t^{\phi} f(x/t^{1/2})$ with an anomalous dimension $\phi$ [B.P. V-L and R.C. Rhoades]. We perform a one-loop renormalization group calculation of this exponent for $d<2$ --- which involves 59 diagrams --- and demonstrate that the anomalous dimension is universal and is due to a renormalization of the initial particle density. Our results are compared to the simulation data.

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