Long-Range and Many-Body Effects in Coagulation Processes

Abstract

We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.

15 pages, 7 figures

References in corpus (6)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Non-perturbative fixed point in a non-equilibrium phase transition
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Non-perturbative Approach to Critical Dynamics
• Non-perturbative renormalization-group approach to lattice models
• Branching rate expansion around annihilating random walks