Internal fluctuations effects on Fisher waves.
We study the diffusion-limited reaction A+A<-->A in various spatial dimensions to observe the effect of internal fluctuations on the interface between stable and unstable phases. We find that, similar to what has been observed in d = 1 dimensions, internal fluctuations modify the mean-field predictions for this process, which is given by Fisher's reaction-diffusion equation. In d>1 the front displays local fluctuations perpendicular to the direction of motion which, with a proper definition of the interface, can be fully described within the Kardar-Parisi-Zhang (KPZ) universality class. This clarifies the apparent discrepancies with KPZ predictions reported recently.
Moro
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Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom. e.moro1@physics.ox.ac.uk