SYMMETRY BETWEEN DIFFUSION-LIMITED COAGULATION AND ANNIHILATION

In homogeneous systems, symmetry is found to exist between the hierarchies of kinetic equations of multipoint joint probability density functions of two diffusion-limited reactions A + A --> A (coagulation) and A + A --> inert (annihilation) by rescaling their multipoint joint density functions. Given one set of the joint density functions, this symmetry allows the solution of the others. A general class of diffusion-limited reactions, which are incomplete reactions between coagulation (with probability p) and annihilation (with probability 1-p), are found to share the same scaling symmetry.