Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations
- 4 November 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 55 (19) , 1947-1949
- https://doi.org/10.1103/physrevlett.55.1947
Abstract
We study interacting particle (spin) systems on a lattice under the combined influence of Glauber (spin flip) and simple exchange (Kawasaki) dynamics. We prove that when the conserving exchanges occur on a microscopically fast scale the macroscopic density (magnetization) evolves according to an autonomous nonlinear diffusion-reaction equation. Microscopic fluctuations about the deterministic macroscopic evolution are found explicitly. They grow, with time, to become infinite, when the deterministic solution is unstable.Keywords
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