We study a two-level transition probability for a finite number of avoided crossings with a small interaction. Landau–Zener formula, which gives the transition probability for one avoided crossing as \(e^{-\pi \frac{\varepsilon ^{2}}{h}}\), implies that the parameter h and the interaction \(\varepsilon \) play an opposite role when both tend to 0. The exact WKB method produces a generalization of that formula under the optimal regime \(\scriptstyle {\frac{h}{\varepsilon ^2}}\) tends to 0. In this paper, we investigate the case \(\scriptstyle {\frac{\varepsilon ^2}{h}}\) tends to 0, called “non-adiabatic” regime. This is done by reducing the associated Hamiltonian to a microlocal branching model which gives us the asymptotic expansions of the local transfer matrices.

我们研究了在交互作用较小的情况下，有限数量的避免穿越的两级过渡概率。Landau–Zener公式给出了一个避免的交叉点的转移概率为\（e ^ {-\ pi \ frac {\ varepsilon ^ {2}} {h}} \），它暗示了参数h和相互作用\（ \ varepsilon \）在两者都趋于0时起相反的作用。确切的WKB方法在最佳状态\（\ scriptstyle {\ frac {h} {\ varepsilon ^ 2}} \）趋于0的情况下对该公式进行了概括。在本文中，我们调查\（\ scriptstyle {\ frac {\ varepsilon ^ 2} {h}} \）趋于0的情况，称为“非绝热”政权。这是通过将关联的哈密顿量简化为一个微局部分支模型来完成的，该模型为我们提供了局部传递矩阵的渐近展开式。