  Population transfer in quantum systems has always been an interesting area in
physics since the introduction of quantum mechanics. In this paper, transition
probabilities for a coupled system consisting of four two - level particles are
studied by solving Landau - Zener Hamiltonian. The effects of the first and
second nearest neighbors interactions are investigated. Presented results
indicate that the second nearest neighbors interactions will decrease the
transition probability when the coupling strength for each neighborhood has the
same sign. The fast sweep effect on transition probability is also studied
here.
