Landau-Zener-Stueckelberg effect in a model of interacting tunneling systems

The Landau-Zener-Stueckelberg (LZS) effect in a model system of interacting tunneling particles is studied numerically and analytically. Each of N tunneling particles interacts with each of the others with the same coupling J. This problem maps onto that of the LZS effect for a large spin S=N/2. The mean-field limit N=>\infty corresponds to the classical limit S=>\infty for the effective spin. It is shown that the ferromagnetic coupling J>0 tends to suppress the LZS transitions. For N=>\infty there is a critical value of J above which the staying probability P does not go to zero in the slow sweep limit, unlike the standard LZS effect. In the same limit for J>0 LZS transitions are boosted and P=0 for a set of finite values of the sweep rate. Various limiting cases such as strong and weak interaction, slow and fast sweep are considered analytically. It is shown that the mean-field approach works well for arbitrary N if the interaction J is weak.