Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

Details Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

2001-04-18

arxiv.org/abs/math-ph/0104024v2

Comm. Math. Phys. 224 (2001)

Physics

Mathematical Physics

Revised version. 19 pages, 2 figures

Scientific paper

10.1007/s002200100535

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.

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