# Geometry of Nonadiabatic Quantum Hydrodynamics

@article{Foskett2018GeometryON, title={Geometry of Nonadiabatic Quantum Hydrodynamics}, author={Michael S. Foskett and Darryl D. Holm and Cesare Tronci}, journal={Acta Applicandae Mathematicae}, year={2018}, pages={1-41} }

The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether’s conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this momentum map, the Hamiltonian is called ‘collective’. Here, we derive collective Hamiltonians for a series of models in quantum molecular dynamics for which the Lie group is the composition of smooth invertible maps and unitary transformations. In this process…

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