Local scattering matrix for a degenerate avoided-crossing in the non-coupled regime.

A Landau–Zener-type formula for a degenerate avoided-crossing is studied in the non-coupled regime. More precisely, a 2 × 2 system of first-order h-differential operator with O (ε) off-diagonal part is considered in 1D. Asymptotic behavior as ε h m / (m + 1) → 0 + of the local scattering matrix near an avoided-crossing is given, where m stands for the contact order of two curves of the characteristic set. A generalization including the cases with vanishing off-diagonals and non-Hermitian symbols is also given. [ABSTRACT FROM AUTHOR]