Berry phase

The Berry phase is a subtle quantum phenomenon where a system's wavefunction gains an extra, measurable trickle of phase after undergoing a cyclic change—meaning the system's parameters return to their original state. Imagine slowly changing the shape of a loop or path and, upon completing the cycle, the system's wave behavior is slightly shifted compared to if it had not undergone the cycle. This phase shift isn't due to energy but results from the geometry of the path taken in the parameter space. The Berry phase has important implications in areas like quantum computing, material science, and fundamental physics.