XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Exact factorization of the time-dependent electron-nuclear wavefunction
E.K.U. Gross
Max Planck Institute for Microstructure Physics, Weinberg 2, D-06120 Halle (Saale), Germany
The coupling between electronic and nuclear motion plays an important role in a variety of phenomena. Prominent examples are superconductivity, the process of vision, and photo-synthesis. Standard approximations such as Ehrenfest dynamics, surface hopping, or nuclear wave-packet dynamics only partially capture the non-adiabatic effects. As a first step towards a full ab-initio treatment of the coupled electron-nuclear system, we deduce an exact factorization of the complete wavefunction into a purely nuclear part and a many-electron wavefunction which parametrically depends on the the nuclear configuration. We derive formally exact equations of motion for the nuclear and electronic wavefunctions [1]. These exact equations lead to a rigorous definition of time-dependent potential energy surfaces as well as time-dependent geometric phases. With the example of the hydrogen molecular ion in a laser field we demonstrate the significance of these concepts in understanding the full electron-ion dynamics. In particular, the time-dependent potential energy surfaces are shown to represent a powerful tool to analyse and interpret different (direct vs. tunneling) types of dissociation processes.

[1] Ali Abedi, Neepa T. Maitra, E.K.U. Gross, PRL 105, 123002 (2010).


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