Magnus approximation for nonadiabatic transitions and neutrino oscillations in matter

Abstract

The Magnus expansion of the time-displacement operator is used to calculate nonadiabatic level crossing induced by a time-dependent Hamiltonian. We consider Hamiltonians that can be represented as a Hermitian 2\ifmmode\times\else\texttimes\fi{}2 matrix. As an interesting nontrivial application an analytic expression for the flavor survival probability is derived for neutrinos which propagate through a matter-enhanced oscillation region.