Time-dependent scattering theory for ODEs and applications to reaction dynamics

We develop a time-dependent scattering theory for general vector fields in Euclidean space. We give conditions that ensure that the wave maps exist, are smooth, invertible, and depend smoothly on parameters. We then discuss the intertwining relations and how they can be used to compute stable/unstable manifolds for time-dependent normally hyperbolic invariant manifolds. The theory is particularly effective for Hamiltonian mechanics. We also give perturbative calculations of the scattering map that are analogous to Fermi's golden rule in quantum mechanics. We apply this theory to a problem in transition state theory concerning the exposure of molecules to a laser pulse for a short time. We present a method to compute invariant manifolds for the laser-driven Henon-Heilies system and give perturbative calculations of the change in the branching ratio.