Propagation of Wave Packets for Systems Presenting Codimension One Crossings

Abstract

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.