Abstract
In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both electronic and nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both electrons and nuclei can be treated quantum mechanically where the guiding waves obey a set of coupled Schrodinger equations (quantum-quantum description) or, alternatively, coupled Schrodinger-Newtonian equations are solved for the quantum-classical approximation. The method takes into account local and nonlocal quantum correlation effects in a self-consistent manner. The general formalism is applied to one- and two-dimensional hydrogen molecules subjected to a strong ultrashort optical pulse. Comparison is made with the results from the "exact" Ehrenfest molecular dynamics for the molecular ionization and for the evolution of the internuclear distance as the molecule dissociates.
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