Dynamics of a pair of magnetic dipoles with nonreciprocal interactions due to a moving conductor

Recently it was demonstrated theoretically and experimentally that the presence of a moving conductor can break the reciprocity in the interactions between magnetic dipoles. In this article we investigate the influence of nonreciprocity on the dynamics of a pair of rigid $XY$ dipoles, which have been realized in experiments. In particular, we focus on the energy nonconservation, which is a consequence of the nonreciprocity. We find that the dynamics indeed has regimes, wherein the kinetic energy grows quadratically. However, whether energy absorption occurs depends strongly on the initial conditions on the dipoles. Simulations for various initial conditions reveal an intricate dependence, resulting in a rich structure of the energy absorbing regime in the initial condition space. Nevertheless, we provide a qualitative explanation of these observations, interpreting the absence of energy absorption as a confinement of the dynamics in phase space.