Constraints on scattering amplitudes in multistate Landau-Zener theory
  We derive a set of constraints, which we will call hierarchy constraints (HCs), on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix. 
N. A. Sinitsyn, J. Lin, and V. Y. Chernyak
quant-ph cond-mat.mes-hall math-ph math.MP nlin.SI