Abstract
In physics, whether classical or quantum, the notion of adiabatic evolution is frequently used. We consider a system whose state depends on an external parameter (the volume of a box containing a fluid, an external field applied to the system, etc.) and we are interested in an evolution in which this parameter changes slowly over time. When the external parameter returns to its initial value at the end of the evolution, it's natural to assume that the system under study also returns to its initial state. However, the result is sometimes more complex than this simple identity; for example, Foucault's pendulum (playing the role of the system) undergoes a rotation of its plane of oscillation after 24 hours, whereas the pendulum's suspension point (playing the role of the external parameter), has returned to its starting point after a complete rotation of the Earth on its axis. In this lecture, we have shown that it is possible to take advantage of the fact that some variables do not return to their initial value, while other variables, which drive the movement of the former, go through a closed cycle. We introduced the notion of Berry phase and showed that it can be used to generate the equivalent of an Aharonov-Bohm phase, even if the particle in question has no electric charge.
