  The Berry curvature is a geometrical property of an energy band which acts as
a momentum space magnetic field in the effective Hamiltonian describing
single-particle quantum dynamics. We show how this perspective may be exploited
to study systems directly relevant to ultracold gases and photonics. Given the
exchanged roles of momentum and position, we demonstrate that the global
topology of momentum space is crucially important. We propose an experiment to
study the Harper-Hofstadter Hamiltonian with a harmonic trap that will
illustrate the advantages of this approach and that will also constitute the
first realization of magnetism on a torus.
