Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-03-09
J. Phys. A: Math. Gen. 37 (2004) 7063
Physics
Condensed Matter
Statistical Mechanics
35 pages (IOP style files included), 10 figures included (as eps files)
Scientific paper
10.1088/0305-4470/37/28/001
The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for 1 <= i < j <= q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as rho(t) ~ t^{- alpha}. For d = 1 the system segregates into single species domains, yielding a different value of alpha for each q; for a simplified version of the model in one dimension we derive alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2, segregation occurs only for q < 1 + (4/d). The only physical realisation of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d >= 2 and q >= 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (alpha = 1) that also characterises the single-species annihilation process A + A -> 0.
Deloubriere Olivier
Hilhorst Hendrik-Jan
T"auber Uwe C.
Washenberger M. J.
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