In classical and quantum mechanics, the geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Hamiltonian. The phenomenon was independently discovered by S. Pancharatnam (1956) in classical optics and by H. C. Longuet-Higgins (1958) in molecular physics; it was later generalized by Michael Berry in (1984), and extended to nonadiabatic cycles by Y. Aharonov and J. Anandan (1987). Its analog in classical mechanics is the Hannay angle.