Statistics of wave functions in coupled chaotic systems

Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wave functions in two coupled disordered or chaotic quantum billiards. We find spatial correlations that are absent in a single chaotic system. Our exact result can be interpreted for small coupling in terms of the hybridization of eigenstates of the isolated billiards. We show that the presented picture is universal, independent of microscopic details of the coupling.