Common
Geometric phase
Phase of a cycle
Geometric phase
In classical and quantum mechanics, the geometric phase (also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry 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. It can be seen in the conical intersection of potential energy surfaces and in the Aharonov–Bohm effect. The geometric phase around the conical intersection involving the ground electronic state of the C6H3F3+ molecular ion is discussed on pages 385–386 of the textbook by Bunker and Jensen. In the case of the Aharonov–Bohm effect...
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