标题： 半经典共振宽度在切向交叉能级处的转变 显示英文标题

标题： Transition of the semiclassical resonance widths across a tangential crossing energy-level

摘要： 我们考虑一个1D$2\times 2$矩阵值算子\eqref{System0}，其对角线项为两个半经典Schrödinger算子，非对角线项有小的相互作用。 当两个势能在接触阶为$n$的拐点处交叉时，对应的两个经典轨迹在交叉能级的相空间中以接触阶为$2n$的方式相交于一点。 我们在入射和出射微局部解之间计算该点的转移矩阵，并将其应用于能量交叉能级处的半经典共振分布。 它用广义Airy函数来描述。 这个结果将\cite{FMW1}推广到切向交叉，将\cite{AFH1}推广到拐点处的交叉。 显示英文摘要

摘要： We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schr\"odinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point with contact order $n$, the corresponding two classical trajectories at the crossing level intersect at one point in the phase space with contact order $2n$. We compute the transfer matrix at this point between the incoming and outgoing microlocal solutions and apply it to the semiclassical distribution of resonances at the energy crossing level. It is described in terms of a generalized Airy function. This result generalizes \cite{FMW1} to the tangential crossing and \cite{AFH1} to the crossing at a turning point.