We analyze the propagation of wave packets through general Hamiltonian systems presenting codimension one eigenvalue crossings. The class of time-dependent Hamiltonians we consider is of general pseudodifferential form with subquadratic growth. It comprises Schrödinger operators with matrix-valued potential, as they occur in quantum molecular dynamics, but also covers matrix-valued models of solid state physics describing the motion of electrons in a crystal. We calculate precisely the non-adiabatic effects of the crossing in terms of a transition operator, whose action on coherent states can be spelled out explicitly.

中文翻译：

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用于呈现 Codimension One Crossing 的系统的波包传播

我们分析了波包通过一般哈密顿系统的传播，呈现出一维一特征值交叉。我们考虑的时间相关的哈密顿量类是具有次二次增长的一般伪微分形式。它包括具有矩阵值势的薛定谔算子，因为它们出现在量子分子动力学中，但也涵盖了描述晶体中电子运动的固态物理学的矩阵值模型。我们根据转换算子精确计算交叉的非绝热效应，其对相干状态的作用可以明确说明。