Kinetics and self-ordering of excitations in low dimensions

Abstract

Diffusion-limited reaction kinetics becomes anomalous not only for fractals, with their anomalous diffusion, but also for low-dimensional (one and two) and disperse media, where the random walk is compact. We focus on annihilation, recombination and trapping reactions under non-equilibrium steady state (steady source) or batch (big bang) conditions. The typical reactions are: A + A --> Products, A + B --> Products and A + T --> T + Products. We are interested in the global rate laws, and their relation to particle-particle distributions (e.g., pair-correlation and nearest-neighbor distribution functions) and in local rate laws (if definable). Anomalous reaction kinetics (more than classical kinetics) is particularly sensitive to initial conditions, source term structure, conservation laws (e.g., equal densities for A and B), excluded volume effects, and medium size, dimensionality and anisotropy. Analytical formalisms, scaling arguments, computer (and supercomputer) simulations and experiments (on chemical and physical reactions) all play an important role in the newly emerging picture.