Landau-Zener Problem for Trilinear Hamiltonians
  We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, a series expansion technique indicates that, when the resonance is crossed slowly, the probability for failure of adiabaticity is directly proportional to the rate at which the resonance is crossed. 
Artur Ishkhanyan, Matt Mackie, Andrew Carmichael, Phillip L. Gould,   and Juha Javanainen