Source-term and excluded-volume effects on the diffusion-controlled A+B→0 reaction in one dimension: Rate laws and particle distributions

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Abstract
For the elementary diffusion-limited reaction A+B→0 on a one-dimensional system of hard-core particles, we show theoretically that the nature of the source term is a fundamental element in the building of the steady state. We also illustrate the importance of the strict conservation of an equal number of A and B at any time, in contrast to a simple conservation on the average. We show how the spatial correlation between members of incoming A-B pairs affects the steady-state distribution. Also, in the case where either first-order decays, such as spontaneous desorption, or vertical annihilation of asymmetric species, are incorporated, the physics is drastically changed. Furthermore, we derive for each case the macroscopic reaction law, and also obtain information on the spatial distribution of the species. The latter shows, in some cases, a macroscopic or mesoscopic segregation phenomenon. We also specify the likely conditions for observing segregation experimentally.