Reaction, Lévy flights, and quenched disorder

We consider the A+A-->Ø reaction, where the transport of the particles is given by Lévy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of reaction. With a model of the disorder that obeys detailed balance, however, the rate of reaction initially increases and then decreases as a function of the disorder strength. The physical behavior obtained with this second model is in accord with that for reactive turbulent flow, indicating that Lévy flight statistics can model aspects of turbulent fluid transport.