Stochastic theory of diffusion-controlled reaction

Abstract

A stochastic theory of a diffusion-controlled reaction is developed with the emphasis on the many-body aspects which rigorous stochastic theories inevitably encounter. The field operator method developed in the previous paper (see ibid., vol.9, no.9, p.1465 (1976)) is extensively used in the analysis. The classical Smoluchowski theory is shown to be strictly valid in the long-time scale, and its relation to the Boltzmann equation is discussed.