Adiabatic and non-adiabatic evolution of wave packets and applications to initial value representations

TL;DR

This paper reviews recent advances in the time evolution of wave packets for pseudo-differential systems, focusing on Schrödinger equations, and explores their applications to approximating unitary propagators, including coherent states and Herman-Kluk methods.

Contribution

It introduces new insights into wave packet evolution for systems with eigenvalue crossings and extends existing approximation techniques to more complex systems.

Findings

Enhanced understanding of wave packet dynamics in systems with eigenvalue crossings

Application of Herman-Kluk approximation to broader classes of equations

Improved methods for approximating unitary propagators in quantum systems

Abstract

We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary propagator. We start with scalar equations, propagation of coherent states, and applications to the Herman-Kluk approximation. Then we discuss the extension of these results to systems with eigenvalues of constant multiplicity or with smooth crossings.