Thermalization of the quantum planar rotor with external potential

We study decoherence, diffusion, friction, and how they thermalize a planar rotor in the presence of an external potential. Representing the quantum master equation in terms of auxiliary Wigner functions in periodic phase space not only illustrates the thermalization process in a concise way, but also allows for an efficient numerical evaluation of the open quantum dynamics and its approximate analytical description. In particular, we analytically and numerically verify the existence of a steady state that, in the high-temperature regime, closely approximates a Gibbs state. We also derive the proper classical limit of the planar rotor time evolution and present exemplary numerical studies to verify our results.