Topological barriers for charged quantum systems

The Aharonov-Bohm effect introduced a surprising influence of topology on the dynamics of quantum systems. The discovery of such a phenomenon unveiled that the evolution of a quantum system with charge traveling around a solenoid is affected by the magnetic flux on it, even though the solenoid only produces electromagnetic field on its interior. Here, making use of the concept of modular variables, which evidence the dynamical nonlocality presented in quantum mechanics, we argue that this effect allows solenoids to be used as barriers of energy for charged quantum systems. Moreover, we present and discuss a thought experiment, as well as its numerical simulation, where a configuration of solenoids inside a cavity can trap some quantum states in a certain subregion of it.