finite size effects of diffusion limited reaction in one-dimension

초록

We have studied the finite size effects and the second order correction of densit decays in a one-dimensional diffusion-limited reaction, A+B-> 0. The density follows a power law like C(t)~t^-x below the crossover time and shows an exponential decay above the crossover time. The crossover time depends on the lattice size and the bias field. We found the second order correction terms of the density as C(t)~t^-x[1+O(t^-y)]. We obtained the exponent of the density decays as x=1/4, y=1/8 without the drift and x=1/3, y=1/24 with the maximum drift by Monte Carlo simulation. The scaling function of the density in the finite lattice is given as C(t)~L^-1/2 f_o (t/L^2) +L^-1/4 f_1(t/L^2) without the drift and C(t)~L^-1/2 f_o (t/L^3/2) + L^-1/12 f_1(t/L^3/2) with the maximum drift where L is the size of the lattice and f_o, f_1 are the caling functions.