Observation of the Topological Change Associated with the Dynamical Monodromy

Classical mechanics is an old theory and new phenomena do not often appear. A recently predicted phenomenon is called ``Dynamical Monodromy.” Monodromy is the study of the behavior of a system as it evolves ``once around a closed circuit”. Systems that do not return to their original state after forming a closed circuit in some space are said to exhibit ``nontrivial monodromy.” One such system is a collection of non-interacting particles moving in a ``champagne bottle” potential. A loop of trajectories of this system exhibits a topological change when each of the particles traverse a monodromy circuit in Energy-Angular Momentum space (any closed path that encloses the singular point at the origin). This system has been realized using a rigid spherical pendulum, with a permanent magnet at its end. Magnetic fields generated by coils are used to create the champagne-bottle potential, as well as drive the pendulum through the monodromy circuit.