On equations of motion on compact Hermitian symmetric spaces

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Abstract
The classical equations of motion on compact coherent state manifolds that have Hermitian symmetric space structure are considered. In the case of Hamiltonians linear in the generators of the group that determines the structure of the manifold of coherent states, the classical motion and the quantum evolution are both described by the same first-order second degree differential equation. The explicit forms of the classical equations of motion as Matrix Riccati equations on the Grassmann manifold GA(Cn) and the coset manifold SO (2n)/U(n), attached to the Hartree–Fock and, respectively, Hartree–Fock–Bogoliubov problem are obtained.

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