Many-body Landau-Zener effect at fast sweep
  The asymptotic staying probability P in the Landau-Zener effect with interaction is analytically investigated at fast sweep, epsilon = pi Delta^2/(2 hbar v) << 1. We have rigorously calculated the value of I_0 in the expansion P =~ 1 - epsilon + epsilon^2/2 + epsilon^2 I_0 for arbitrary couplings and relative resonance shifts of individual tunneling particles. The results essentially differ from those of the mean-field approximation. It is shown that strong long-range interactions such as dipole-dipole interaction (DDI) generate huge values of I_0 because flip of one particle strongly influences many others. However, in the presence of strong static disorder making resonance for individual particles shifted with respect to each other the influence of interactions is strongly reduced. In molecular magnets the main source of static disorder is the coupling to nuclear spins. Our calculations using the actual shape of the Fe-8 crystal studied in the the Landau-Zener experiments [Wernsdorfer et al, Europhys. Lett. 50, 552 (2000)] yield I_0 that is in a good agreement with the value extracted from the experimental data. 
D. A. Garanin and R. Schilling