  Using the supersymmetry technique, we calculate the joint distribution of
local densities of electron wavefunctions in two coupled disordered or chaotic
quantum billiards. We find novel 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.
