Geometry of quantum Riemannian Hamiltonian evolution

This paper concerns a study of the quantum mechanical extension of the work of Horwitz et al. [Phys. Rev. Lett. 98, 234301 (2007)] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples; these show that the quantum mechanical extension of the classical method, for which trajectories are plotted as expectation values of the corresponding quantum operators, appears to work well, providing results consistent with the corresponding classical problems. The results appear to provide a new contribution to the subject of quantum dynamical instability.