Abstract
We show that the decay of the density of active particles in the reaction in one dimension, with exclusion interaction, results in logarithmic corrections to the expected power law decay, when the starting initial condition (i.c.) is periodic. It is well known that the late-time density of surviving particles goes as with random initial conditions, and as with alternating initial conditions (). We show that the decay for periodic i.c.'s made of longer blocks () do not show a pure power-law decay when is even. By means of first-passage Monte Carlo simulations, and a mapping to a -state coarsening model which can be solved in the independent interval approximation (IIA), we show that the late-time decay of the density of surviving particles goes as for even, but as when is odd. We relate this kinetic symmetry breaking in the Glauber Ising model. We also see a very slow crossover from a regime to eventual behavior for i.c.'s made of mixtures of odd- and even-length blocks.
- Received 3 October 2017
DOI:https://doi.org/10.1103/PhysRevE.97.042118
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