Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

TL;DR

This paper refines the time-dependent Born-Oppenheimer theory by distinguishing adiabatic decoupling from semiclassical dynamics within energy bands, accounting for band crossings and Berry connection effects.

Contribution

It provides a detailed analysis of adiabatic decoupling and semiclassics in the presence of band crossings, with results valid up to the first crossing.

Findings

Effective Schrödinger equation for nuclei derived

Inclusion of Berry connection contributions

Results valid up to first band crossing

Abstract

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schroedinger equation for the nuclei, including contributions from the Berry connection.