A+A→∅ model with a bias towards nearest neighbor.
We have studied the A+A→∅ reaction-diffusion model on a ring, with a bias ε(0≤ε≤0.5) of the random walkers A to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The z exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at ε=0 to the mean-field value of unity for any nonzero ε. We study the problem analytically using independent interval approximation and compare the scaling results with those obtained from simulation. The distribution P(k,t) (per site) of the spacing between two walkers is given by t(-2/z)f(k/t(1/z)) and is obtained both analytically and numerically. We also obtain the result that εt becomes the new time scale for ε≠0.
Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.
Parongama
P
Sen
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.
Purusattam
P
Ray