Internal Fluctuations Effects on Fisher Waves

We study the diffusion-limited reaction $A+A\leftrightarrow A$ 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 $d=1\mathrm{}$ dimensions, internal fluctuations modify the mean-field predictions for this process, which is given by Fisher’s reaction-diffusion equation. In $d>\mathrm{}1\mathrm{}$ 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.