Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

Abstract All currently known exactly solvable multistate Landau–Zener (MLZ) models are associated with families of operators that commute the MLZ Hamiltonians and depend on time linearly. There can also be satisfy integrability conditions but quadratically. We show that, among systems, such time-quadratic much more common. demonstrate then generally lead to constraints independent variables parametrize scattering matrix. Such asymptotically exact expressions for transition probabilities in adiabatic limit a three-level model. New complex fully systems found.