In mechanics, the Geometric phase, or the Pancharatnam-Berry phase (named after S. Pancharatnam and Sir Michael Berry), also known as the Pancharatnam phase or Berry phase, is a phase acquired over the course of a cycle, when the system is subjected to cyclic adiabatic processes, resulting from the geometrical properties of the parameter space of the Hamiltonian. The phenomenon was first discovered in 1956, and rediscovered in 1984. It can be seen in the Aharonov-Bohm effect and in the conical intersection of potential energy surfaces. In the case of the Aharonov-Bohm effect, the adiabatic parameter is the magnetic field inside the solenoid, and cyclic means that the difference involved in measuring the effect by interference corresponds to a closed loop, in the usual way. In the case of the conical intersection, the adiabatic parameters are the molecular coordinates. Apart from quantum mechanics, it arises in a variety of other wave systems, such as classical optics. As a rule of thumb, it occurs whenever there are at least two parameters affecting a wave, in the vicinity of some sort of singularity or some sort of hole in the topology.

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