  We study the quantum behaviour of a binary mixture of Bose-Einstein
condensates (BEC) in a double-well potential starting from a two-mode
Bose-Hubbard Hamiltonian. We focus on the small tunneling amplitude regime and
apply perturbation theory up to second order. Analytical expressions for the
energy eigenvalues and eigenstates are obtained. Then the quantum evolution of
the number difference of bosons between the two potential wells is fully
investigated for two different initial conditions: completely localized states
and coherent spin states. In the first case both the short and the long time
dynamics is studied and a rich behaviour is found, ranging from small amplitude
oscillations and collapses and revivals to coherent tunneling. In the second
case the short-time scale evolution of number difference is determined and a
more irregular dynamics is evidenced. Finally, the formation of Schroedinger
cat states is considered and shown to affect the momentum distribution.
