  We determine transition probabilities in two exactly solvable multistate
Landau-Zener (LZ) models and discuss applications of our results to the theory
of dynamic passage through a phase transition in the dissipationless quantum
mechanical regime. In particular, we show that statistics of particles in a new
phase demonstrate scaling behavior. Our results also reveal a symmetry that we
claim is a property of a large class of multistate LZ models, whose explicit
solutions are not presently known. We support our arguments by direct numerical
simulations.
