Stochastic coupling in two modes systems: the weak-strong coupling transition

We investigate the weak-strong coupling transition of two linearly coupled systems under the influence of a phase fluctuating coupling. In the weak coupling regime the exponential decay of quantum properties is well known. A different scenario occurs in the strong coupling regime, the inhibition of the dynamics which tends to "freeze" as the ration between coupling strength and average phase fluctuation time increase. Exciton-polariton oscillations and the self-trapping phenomenon in Bose-Einstein Condensate qualitatively illustrate the weak and strong regimes respectively.