The geometric phase

In 1983 the author found a geometric effect exists in the quantum waves that describe matter and its interactions on the smallest scales. In this case the anholonomy appears in a system's wave function (the mathematical description of a system's physical state) after the system has been transported around a cyclic circuit on an abstract surface in parameter space. He calls this anholonomy the geometric phase, because it manifests itself specifically as a shift in the wave function's phase: a quantity that describes where the wave function is in its oscillatory cycle at any given time and place. It so happens that the geometric phase provides an elegant explanation of various quantum-mechanical phenomena in systems whose environment undergoes a cyclic change: neutrons that pass through a helical magnetic field, polarized light in a coiled optic fiber and charged particles circling an isolated magnetic field. Perhaps more surprising is the fact that the geometric phase can also be generalized to applications in classical physics. Among other things, it offers a new way to describe the behavior of such textbook objects as pendulums