Exact results for models of multichannel quantum nonadiabatic transitions

Original · EN

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form H(t) = A +B t + C/t, where t is time and A, B, C are Hermitian N× N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t → -∞. This allows one to continue such solutions analytically to t → +∞, and connect their asymptotic behavior at t → -∞ and t → +∞. This property becomes particularly useful when a model shows additional discrete symmetries. In particular, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.