A geometric phase is a quantum phase associated with the geometry of a path of state rays, after separating the dynamical phase. The Berry phase is its cyclic case governed by the adiabatic theorem; more general cyclic evolution can also have a geometric phase.
Geometric phase, also known as the Berry phase, is a phenomenon in quantum mechanics and more broadly in physics that describes how the state of a quantum system changes when it undergoes adiabatic (slow) evolution along a closed path in parameter space.
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