We consider a 2 × 2 system of 1D semiclassical differential operators with two Schrödinger operators in the diagonal part and small interactions of order hν in the off-diagonal part, where h is a semiclassical parameter and ν is a constant larger than 1/2. We study the absence of resonance near a non-trapping energy for both Schrödinger operators in the presence of crossings of their potentials. The width of resonances is estimated from below by Mhlog(1/h) and the coefficient M is given in terms of the directed cycles of the generalized bicharacteristics induced by two Hamiltonians.

中文翻译：

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具有能级交叉的薛定谔算子系统的无共振域

我们考虑一个2 × 2一维半经典微分算子系统，对角线部分有两个薛定谔算子，阶数交互很小Hν在非对角线部分，其中H是一个半经典参数并且ν是一个大于1/2. 我们研究了两个薛定谔算子在存在电位交叉的情况下在非俘获能量附近没有共振。共振的宽度由下式估计米H日志(1/H)和系数米是根据两个哈密顿量诱导的广义双特征的有向循环给出的。