Kinetic regimes and cross-over times in many-particle reacting systems

¹ Department of Chemical Engineering, Columbia University New York, NY 10027, USA
² Department of Physics, Columbia University - New York, NY 10027, USA

Received: 8 June 1998
Accepted: 21 December 1998

Abstract

We study kinetics of single-species reactions ("") for general local reactivity Q and dynamical exponent z (rms displacement .) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above the critical value , kinetics are always mean field (MF). Below d_c, the density n_t initially follows MF decay, . A 2-body diffusion-controlled regime follows for strongly reactive systems () with . For , MF kinetics persist, with . In all cases at the longest times. Our analysis avoids decoupling approximations by instead postulating weak physically motivated bounds on correlation functions.