Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems

Details Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems

1998-05-27

arxiv.org/abs/cond-mat/9805356v2

Europhys. Lett., v.45, p.653, 1999

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figure, uses bulk2.sty, minor changes, submitted to Europhysics Letters

Scientific paper

10.1209/epl/i1999-00217-9

We study kinetics of single species reactions ("A+A -> 0") for general local reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above the critical value d_c=z, kinetics are always mean field (MF). Below d_c, the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~ n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q

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