Geometric Phase

The geometric phase is a phenomenon in physics where a system's state gains a sort of "extra twist" or subtle change after undergoing a cyclic process—like moving around a loop—without changing its fundamental properties. Think of it as a hidden "memory" of the path taken, not just the start and end points. This effect appears in contexts like optics, quantum mechanics, and wave behavior, influencing how systems behave in ways that are purely due to their journey through a space of possibilities, rather than just their initial and final states.