Physics and Astronomy Calendar

We consider diffusion-limited pair annihilation reactions of q species: A_i + A_j -> 0 (1 <= i < j <= q) in d space dimensions. Starting from the master equation associated with this stochastic process, we employ various tools including mean-field and scaling arguments, van Kampen's fluctuation expansion, mapping to a field theory representation, and Monte Carlo simulations to study the system's asymptotic behavior. For equal initial densities as well as uniform reaction and diffusion rates for each species, the total particle density decays according to a power law ~ t^{-a(q)} at long times. In one dimension, segregation into single-species domains occurs, and we obtain a(q) = (q-1)/2q. We find that the segregation phenomenon is limited to dimensions d < d_s = 4/(q-1). For d > d_s the system remains well mixed, and for d > 2 the density decays with the universal mean-field exponent a = 1 that also characterizes single-species pair annihilation. Certain symmetric special cases will be discussed as well, and intriguing connections to quantum many-particle systems and spin chains will be pointed out.

References:
O. Deloubriere, H.J. Hilhorst, and U.C.T., Multispecies pair annihilation reactions, Phys. Rev. Lett. 89, 250601 (2002) cond-mat/0209471;
H.J. Hilhorst, O. Deloubriere, M.J. Washenberger, and U.C.T., Segregation in diffusion-limited multispecies pair annihilation, J. Phys. A: Math. Gen. 37, 7063 (2004) cond-mat/0403246;
H.J. Hilhorst, M.J. Washenberger, and U.C.T., Symmetry and species segregation in diffusion-limited pair annihilation, J. Stat. Mech. P10002 (2004) cond-mat/0409079